The 26-year-old Corinthians and former AC Milan forward has spent the last two seasons on loan at Sao Paulo.
"I really want to play for Chelsea," he told reporters.
"I need to play. I'm so happy," the Brazil international said, adding that Chelsea was his "new home".
Pato joined Milan as a 17-year-old in 2007 and played over 100 games for the Italian Serie A club before returning to Brazil in 2013.
He has played 27 times for his country and scored 10 goals, his last appearance coming in 2013.
"Thanks Chelsea for the support and thanks for my fans," he said. "I want to know my new friends, the new players and the team."
Champions Chelsea, 13th in the Premier League, have a shortage of attacking firepower in their squad with Diego Costa and Loic Remy the only experienced strikers available to interim manager Guus Hiddink.
(Reporting by Ed Osmond; editing by Toby Davis)
