Not the "official" adoption, but after Constantine's conversion in 311 CE. His Edict of Milan reaffirmed religious tolerance throughout the Empire and enabled Christians to practice openly. Constantine embarked on a program of building new edifices for Christian worship. Up until that point, the places where they worshiped had been very ad hoc, with no unifying plan. Many were converted out of domestic dwellings and were designed to be concealed from prying eyes.
As Constantine considered what the new edifice would look like, he understandably turned away from Roman temple design. Pagan temples are focused on the exterior: the altar is the heart of worship, and that was always outside; the interior of a pagan temple is to house the cult statue, and to house the possessions of the god; it is not meant to be packed with worshipers. As a mystery cult, Early Christianity had the opposite focus: it was interior-looking, focused on the baptistry, and its meeting places needed to house worshipers inside, in front of a stage or area of display for speakers and baptisms.
Constantine decided (or embraced the idea, maybe) that the Roman secular building form of the basilica should be re-purposed or borrowed for Christianity's new "public" architectural form. It had a tall, spacious interior; it had a long axis, and a "stage" area in the apse at one end (or both) where, in the past, Roman praetors had sat for trials. It thus carried an air of official authority. It had always been an opulent and majestic structure by default in the Roman empire, and also ubiquitous, being one of the basic buildings in any town wishing to seem more "Roman," along with the forum and the Capitolium. Its construction was also usually associated with rulers and authority, from local town elite to Emperor.
And so Constantine built one of the first "churches" in Rome, the "Old St Peter's".