The club reached an agreement with La Liga rivals Valencia over the transfer of the Argentina international on Sunday, with the 26-year-old having a medical with the club on Tuesday.
Banega had been at the Mestalla since 2008 but spent last term on loan at Newell's Old Boys in his homeland, featuring 20 times in all competitions and scoring once.
He also spent a season on loan at Atletico Madrid during his time with Valencia, but revealed he was looking forward to joining up with former boss Unai Emery at Sevilla.
"I want to work every day to earn a place and repay the trust that this club has given me," he said.
"Valencia is already past. I appreciate all that happened there, but now I have to focus on my new club."
Fellow new arrival Gerard Deulofeu - on a season-long loan from Barcelona - is also looking forward to playing alongside his new team-mates.
"[I am] Very happy to be here," he added. "[Barcelona coach] Luis Enrique told me that I would not have minutes and from the first moment I had in my mind to come to Sevilla.
"It is a very good club that has high expectations and hopefully we can make a great year together."
Sevilla, last season's UEFA Europa League winners, have been active in the transfer market during the close-season, with Banega the eighth arrival as Emery looks to cope with the losses of Ivan Rakitic and Alberto Moreno, who have joined Barcelona and Liverpool respectively.
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