Boris Eguize came from a wealthy Karaite family. In the Russian Empire, he received an excellent art education. First, he studied at Odessa Art School with Kyriak Kostandi, who trusted Eguize to lead his class during his frequent absences due to illness, and then at two academies, in St. Petersburg (with Pavel Chistyakov and Vasily Vereshchagin) and Paris (with Jean Paul Laurence and Jean-Joseph Benjamin-Constant). In addition, his progress was enhanced by frequent travels abroad, working in art galleries and museums, as well as the zealous study of other masters of portraiture such as Diego Velázquez, Rembrandt van Rijn, Anthony van Dyck and Titian. Eguize regularly participated in various exhibitions from 1898 onwards and in particular was a permanent participant in the exhibitions of the Association of South Russian Artists.

He moved to Turkey in 1922 and lived there for almost seventeen years. While living in Istanbul, he actively advanced in the field of portraiture, and already in 1923, after he had become a member of the Union of Russian Painters in Constantinople, he was described as "an absolutely valuable acquisition" and "an extremely interesting fellow member" (Ted’, “K Vystavke Hudojnikov”). It is known that he was only able to carry a few large portraits with him, all other canvases remained in the former Russian Empire. One of these artworks, Billet-doux, was exhibited by Eguize at the Union’s exhibition on 29 June 1923 in one of the YMCA venues (Kabristan Street 40, Pera/Beyoğlu). A total of 15 of his paintings were presented at the YMCA, including A Thoughtful Young Girl, later published in the almanac Les Russes sur le Bosphore, and The Nude, which was praised for "beauty of form, truthfulness and pleasant colouring". Although many works by other portrait painters were shown at the exhibition, critics unanimously praised Eguize as the best artist. According to the authors of the almanac Les Russes sur le Bosphore, almost all his portraits were worthy of “decorating” the best art galleries and were "full of light and airiness" but "there were almost no exhibitions in Constantinople at that time and local people did not show much interest in his painting". Nevertheless, there is also a contrary opinion. Thus, for example, according to a small note of Lithuanian Art, in Istanbul he taught students at a private art studio (the studio's existence was confirmed by Marina Sığırcı) and became famous as a portrait artist, whom the ambassadors of various embassies frequently asked to paint portraits.

After Istanbul, Eguize went to Paris but stayed there only for a short time and finally moved to his sister in Vilno (today's Vilnius). His sister Vera was the wife of the famous leader of the Polish and Lithuanian Crimean Karaites community, Seraya Shapshal. There Eguize painted portraits of the local nobility and representatives of the Jewish community. In 1944 he joined the Union of Painters of the Lithuanian SSR. It is also interesting that the artist bequeathed 47 of his works to Odessa, but the local museum refused to accept them (possibly because it would have been necessary to pay for the transportation). A few years later, the museum management revised its decision, but it was too late (Anonymous, “Boris Isayevich Eguize”). Now the paintings are in private collections, in the homes of the artist's relatives and friends.