Miami has yet to make a corresponding move, but quarterbacks Brock Osweiler and David Fales seem to be the most in danger of being waived after Falk was claimed.
Head coach Adam Gase told the Florida Sun-Sentinel the plan throughout preseason was to keep three quarterbacks.
"At the end of the day, you talk about that being one of the most important positions in professional football," Gase said. "Our thought process is we're going to try to develop guys and get them ready to go, and if we have a situation where we need the next guy to get up, we want to make sure we have the right guy."
Tennessee selected Falk out of Washington State, in the 2018 NFL Draft in the sixth round. He completed 68.3 percent of his passes for 14,481 yards and 19 touchdowns for the Cougars.
The Dolphins open the regular season on Sunday against the Titans at Hard Rock Stadium in Miami.