Vietto was involved in Atletico's preparations for the new season, but the 24-year-old continued to be linked with a move away from the Wanda Metropolitano.
The Argentine arrived at Atletico in 2015 off the back of an impressive season at Villarreal, but he has struggled in the Spanish capital and spent the second half of last term on loan at Valencia - scoring five times in 18 appearances.
Fulham confirmed a deal for the attacker at little past 7pm on Thursday night, and he could make his debut for the Cottagers in their Premier League clash with Crystal Palace on Saturday afternoon.
"I'm very happy to come to the club and sign. I'm very excited to get started with the team tomorrow. It's an important change for me because this is my first experience here in England. I hope to do as well as possible," Vietto told Fulham's official website.
Fulham are also believed to be trying to tie up a couple more loan deals before the night is out.