Scott said in a statement issued Wednesday that the two major league clubs "have chosen to stay in Florida for the next 30 years."
The statement did not refer specifically to the teams' intention to set up a shared spring training site in West Palm Beach, where officials have been making plans to build a baseball stadium.
In Scott's news release, Astros owner Jim Crane was quoted as thanking Palm Beach County and West Palm Beach officials for making the deal possible.
The Nationals currently train in Viera, along Florida's Space Coast, while the Astros train in Kissimmee, south of Orlando.
Both teams' current leases expire next year.