The deal includes an option for a permanent transfer to the MLS club.
"Matthew is an exciting, young player who has already gotten a lot of experience in a number of different leagues," Earthquakes general manager Chris Leitch said in a news release Thursday.
"He has also played at the international level and was a big part of the U.S. Gold Cup victory in 2021. With his ability to play multiple positions, he is going to be an important addition to our attacking core."
From Southern California, Hoppe has earned eight caps with the USMNT. He scored the game-winning goal against Jamaica in the 2021 Gold Cup quarterfinals.
Hoppe enjoyed a breakout spell with Schalke in 2021, when he became the first American to score a hat trick in the Bundesliga.
However, he struggled for playing time following subsequent moves to Mallorca and Middlesbrough, making a combined 13 appearances across both clubs.
Information from Reuters was used in this report.