In 1841, Alexey graduated from military school, serving in the Russian Navy and travelling with the fleet to many countries. In 1849, he started to attend classes of the Saint Petersburg Academy of Arts, where he studied under Maxim Vorobiev. The young painter was greatly influenced by Ivan Ayvazovsky. In 1853, he finished the Academy with a major Gold medal. He retired as a navy officer and was appointed an artist to the Navy headquarters.
From 1854 to 1860, he travelled around Europe and worked prolifically. In Rome, he was acquainted with Alexander Ivanov, who convinced Bogolyubov to focus more on drawing. In Düsseldorf, Bogolyubov took classes from the painter Andreas Achenbach. In Paris, he admired the artists of the Barbizon School. French painters Camille Corot and Charles-François Daubigny were good friends and collaborators with Bogolyubov. He also painted the frescoes in the Alexander Nevsky Cathedral.