He has often looked devoid of confidence in front of goal in England, losing the faith of both former Chelsea coach Antonio Conte and current Blues boss Maurizio Sarri.
"I'm absolutely made up and so proud to be here," he told a news conference after officially signing his deal
"There were other offers but all that stopped when Atletico came into the equation. I'm here and it's brilliant. I can't wait to train with my new teammates."
A boyhood Atletico fan, Morata spent four years in the club's academy before joining Getafe's youth setup in 2007 and later Real Madrid's.
He spent four years with the Real first team between 2010 and 2014, moving to Juventus for two years before returning to the Spanish capital. He then joined Chelsea in 2017.
"It means a lot for me to be here, with people who know me and I can only give my thanks," he added.
"I didn't need convincing (by coach Diego Simeone) to join. He knew that destiny was calling me here. I can't wait to get started and to play for him."
Morata could make his debut on Sunday's at Real Betis, with the intriguing prospect of a Madrid derby against Real a week later, before his other former club Juventus, visit in their Champions League last 16 first leg next month.