It is believed that the 24-year-old Frenchman has signed a three-year deal with the option of a fourth should he prove successful.
Boro agreed the fee with the Gunners and personal terms with the player some time ago but had to wait until he returned from holiday to finalise the transfer.
Gareth Southgate's first summer signing was Jonathan Woodgate, who completed a permanent £7million move from Real Madrid in April which comes into effect on July 1.
With Turkey international Tuncay Sanli due on Teesside this week to seal his free transfer from Fenerbahce, Southgate has also moved quickly to plug the gap left by Mark Viduka.
Aliadiere has been in Boro's sights for the last 12 months, but injuries to Thierry Henry and Robin van Persie meant Arsene Wenger was unwilling to part with him during the January transfer window.
However, his opportunities at the Emirates Stadium were limited despite a major contribution to the Gunners' run to the Carling Cup final.
In all the former France Under-21 international started only 19 senior games and made a further 32 appearances as a substitute during his seven years with Arsenal, scoring nine goals.
Twelve of those starts came last season when, with 11 outings as a substitute, he scored four times, all of them in the League Cup.