"Now I am a City player," Aguero, who is known as "Kun" after a Japanese cartoon character, said on the feed, which can be reached via a link on his official website.
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"Happy to be at this club and in this city," added the 23-year-old. "Thank you to everyone for the welcome and the reception."
A separate statement posted on his website later on Wednesday said he had passed a medical and signed his contract.
One of the most sought-after forwards in world football, Aguero announced at the end of May he wanted to leave Atletico, who unlike City missed out on a place on next season's Champions League, Europe's elite club competition.
Spanish media reported the English Premier League side had agreed to pay 45 million euros to secure his services and he is expected to replace unsettled compatriot Carlos Tevez.
Juventus had also been chasing Aguero, who upstaged team-mate Lionel Messi of Barcelona at the Copa America by scoring three times in four games.
He was one of the few bright spots for the hosts, who bowed out at the quarter-final stage after a penalty shootout defeat to eventual champions Uruguay.
Married to one of Diego Maradona's daughters, Aguero has spent five seasons at Atletico, where he won the Europa League in 2009/10.
He was raised at Independiente where he made his professional debut as a 15-year-old.
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