Between Kağızman and Karakurt, the district's main road runs along the bottom of the Aras valley, but this is probably a modern route - the medieval track (an important route linking the Ararat plain with Erzurum and beyond) probably ran over the hills to the north of the valley. If this was the case then Çengelli would have been located along that medieval route.

Çengelli lay in a district of Armenia known as Gabeghenk, which included the town of Kaghzuan (modern Kağızman), and was a part of a larger Armenian province known as Ayrarat. This district was initially a Mamikonian possession, but in the 9th century it became part of the territory of the Bagratids of Ani. When Kars split away from Ani, Gabeghenk became part of the Kars kingdom.

An inscription on the west facade of the church is dated 1030 according to some readings, but 1362 according to others. It mentions the building's founder, Egnatio, states that it was part of a monastery, indicates that it was under the jurisdiction of the Georgian patriarchate, and seems to mention the old name of the site, Lenamori. This could mean either that the monastic community was a colony of ethnic Georgians, or that it was used by Armenians adhering to the Georgian (Chalcedonian) Church. There were certainly Armenians living in the settlement at that time - at the end of the 19th century several medieval khatchkars bearing Armenian inscriptions were noted, including one dated 989 and another dated 1024. Another inscription in Georgian, under the church's south cornice, says "Christ, have mercy on Malakozia who built this church".

Regardless of whether Çengelli was used by Georgian settlers or by Chalcedonian Armenians, the church displays a very strong Georgian influence in its architecture. Tao-Klardjeti, a region now within northeastern Turkey, was the closest Georgian-controlled area to Çengelli, and many features found in the Çengelli church can also be seen in the surviving Georgian churches of this region. It is likely that the builders of this church came from Tao-Klardjeti. On stylistic grounds, and based on the dates of the Tao-Klardjeti churches, the Çengelli church probably dates from the late 10th or early 11th century.

In 1907 a Russian archaeological expedition investigating Tao-Klardjeti also visited Çengelli. Led by the Georgian scholar E. S. Taqaishvili, it included the architect E. Kalgin who measured the Çengelli church and later produced a plan, elevations, and sectional drawings of it.

By the end of the 19th century the majority of the village's population was Armenian. They were adherents to the Armenian Church rather than the Georgian one, and called the church St. Astuacacin (Holy Mother of God). This Armenian population was deported to Armenia in 1920 when this district became part of Turkey after the First World War. The village's present inhabitants, like most of the villages in this district, are Kurds - probably recent immigrants from either Erzurum or Doğubayazit. They use the church as a communal barn.

The dome has a cylindrical drum that is decorated with a blind arcade of 16 arches. The arches are "supported" on twin colonettes with capitals that are shaped rather like tulips. Some of the colonettes have zigzag banding on them. The surface under each arch alternates between windows and triangular niches. There are eight windows in total (Thierry erroneously says that there are six). Above this arcade, and forming the cornice to the roof, is a twisted moulding and a frieze of stylised triangular palmettes with concentric ribs. The design of these palmettes (see the drawing below, by Thierry) is exactly comparable to those found in the same position on the Işhan cathedral in Tao-Klardjeti.

The roof of the cupola, which is not quite conical, has a covering of glazed roof tiles in the same manner as many of the Tao-Klardjeti churches.

Compared to the richly sculptured drum, the lower parts of the church have an extremely austere aspect. Most of the windows have only a simple hooded moulding, and even the roof cornice is plain. The structure rests on a foundation with three steps.

The church has two entrances - one is in the middle of the west wall of the west arm, and a second is in the south wall of the west arm, near its junction with the south arm. Both these doorways are extremely plain, surprisingly so when compared against the doorways of the churches in Ani. The tympanum over the west door has a frame composed of a band of palmettes that are identical to those on the drum, bordered by a double twisted moulding. On this tympanum is a rather crudely carved inscription in Georgian - the inscription from 1030/1362 that was mentioned earlier.

The east facade has a blind arcade of three arches. These are far heavier and more cantilevered than their equivalents at Ani, but are similar to those found on Georgian churches in Tao-Klardjeti. There are also arcades, on a smaller scale, on the north and south walls of the east arm - these arcades are now mostly hidden behind the later corner chambers.

The corners of the central square are reinforced by engaged piers with semi-columns. The capitals of these are formed from concentric cylinders; similar capitals can be seen inside the Saint Sergius church at Khtzkonk monastery. These capitals support slightly pointed vaulting over the church's four arms.

The drum is supported on squinches, a feature that is far more common in Georgian than Armenian architecture. The surfaces of the two southern squinches are carved with conch-like ribs, the two northern ones are plain.

The interior of the drum has an exceptionally complex and entirely unique design. It is formed from 8 semicircular exedrae, each containing a window. The broad edge that separates each exedra takes the form of a pilaster with two engaged colonettes. The base of each pilaster is hollowed out to form a niche, the resulting space being filled with a short, free-standing, column with a capital. These columns rest on a broad cornice that runs around the base of the drum. This arrangement is not known in any other Armenian or Georgian church, but may be stylistically connected to the columns found in the apses of the Georgian churches at Işhan and Bana (Banak). In Kalgin's reconstruction of the circular church at Bana, the interior of the drum has a form similar to that of the Çengelli church.

There are no frescoes inside the church, nor any indications that there ever were any. It is in this aspect that Çengelli differs most from the Georgian churches of Tao-Klardjeti and from Georgian churches in general. This absence of paintings suggests a definite Gregorian Armenian influence since, in the kingdom of Ani during the 10th and 11th century, paintings were almost entirely excluded from Armenian religious monuments. Their absence also indicates that the alternative date that is proposed for this church (the late 13th century) is unlikely to be correct. A church from this later period would probably have had frescoes.