According to Gianluca Di Marzio, the two clubs finalised terms on Friday and the player is signing a five-year deal.
Atalanta and Lokomotiv have been exchanging the final documents ahead of an official announcement.
Miranchuk will leave Lokomotiv after spending his entire professional career at the club.
He made his first team debut in 2013 and in 228 appearances has scored 43 goals and contributed 45 assists.
In the early stages of the new Russian Premier League season, Miranchuk has two goals and one assist.
Lokomotiv have now announced the sale of Miranchuk to Atalanta subject to him passing his medical.
🚨Lokomotiv and @Atalanta_BC have reached an agreement in principle over the transfer of Aleksey Miranchuk!
— FC Lokomotiv Moscow (@fclokomotiv_eng) August 30, 2020