A source tells ESPN's Jeff Carlisle that the transfer is "close" to $4.1 million and includes add-ons. The fee was first reported by MLSsoccer.com.
Tessmann, 19, was just in his second season with FCD's first team, after having come up through Dallas' academy since 2016. He's made a total of 28 league and playoff appearances, 16 of them starts, spending the bulk of his time in the center of the midfield.
"Ever since I came to the academy at 14 years old, FC Dallas was developing me, honing my skills and making me a better young man. I knew an opportunity like this would be possible and it was always in the back of my mind, only because FC Dallas was there," Tessmann said in a club statement. "I'm excited for this new experience. It's going to be a good journey. This is not a goodbye. It's an 'I'll see you soon'."
Tessmann won the Golden Ball after leading FC Dallas to the U18/U19 Academy Championship in 2019.
At the international level, Tessmann made his only USMNT appearance at senior level back on Jan. 31, coming on as a 78th minute substitute in a 7-0 win over Trinidad and Tobago. He also made three appearances for the U.S. U-23 team during the Olympic qualifying tournament last March.
He joins a Venezia side that was just promoted to Serie A, making the upcoming 2021-22 campaign its first in the Italian top flight since the 2001-02 season. The club is owned by American Duncan Niederauer, who also serves as Venezia's president and CEO.
Tessmann is the latest FCD alum to a European club, a group that includes Bryan Reynolds at AS Roma, Chris Richards at Bayern Munich, Reggie Cannon at Portuguese side Boavista, and Weston McKennie, now at Juventus.
The Birmingham, Alabama, native was a two-sport star growing up and had originally signed a letter of intent to play college football at Clemson under head coach Dabo Sweeney, who is also Tessmann's godfather.