The 29-year-old only joined Atletico last summer from Bayern Munich and scored 20 goals in 43 games for the Spanish side.
He has agreed a four-year deal with the beaten Champions League finalists, who said the fee could rise to £15m.
"I like Juventus and I like the city [Turin]. I hope I will be happy here. I will fight for my new team," he said.
It is the third time in four years Mandzukic has joined a side straight after they lost the Champions League final, following his 2012 move to Bayern and last summer's switch to Atletico.
Juventus striker Carlos Tevez, their top scorer last season with 20 Serie A strikes, has been linked with a move away from the Italian champions.
Argentine legend Diego Maradona hinted recently he could rejoin Boca Juniors.
Find all the latest football transfers on our dedicated page.
Juventus have signed Croatia striker Mario Mandzukic from Atletico Madrid for £13.6m.