Vietto joined Atletico from Villarreal after impressing in the 2014-2015 campaign, his first in LaLiga, but he failed to suitably adapt to the style of Diego Simeone's side and never truly established himself.
A loan move to Sevilla followed in the 2016-2017 season and he got off to a fine start, scoring twice on his LaLiga debut - a 6-4 win over Espanyol.
However, he soon fell out of favour at the Ramon Sanchez Pizjuan as well, before then struggling on loan at Valencia last season.
Vietto returned to Atletico in January in what was essentially a final chance to carve out a career in the Spanish capital, but he failed to score in six appearances.
Fulham has the option to make the deal permanent should the 24 year-old impress in London.
Fosu-Mensah also joins the Craven Cottage club on loan, though there is no such purchase option included in that deal.
The Dutchman spent last season at Crystal Palace and had been tipped to play at role at Old Trafford this term, but with Matteo Darmian potentially staying put and Diogo Dalot arriving from Porto, first-team opportunities at right-back may have been limited.