"Good luck to you in Milwaukee! "Very deserving to you and your family."
The Dallas Mavericks, Sacramento Kings and the Atlanta Hawks were all reportedly in the hunt for Dellavedova.
Cavaliers had offered Dellavedova $US1.4 million to retain his services and they could keep him if they match the Bucks' offer.
Dellavedova, who is in Australia preparing for the Olympics, and the Bucks will not be able to sign the contract until July 7.
However, as the tone of James' tweet suggests, it is unlikely the Cavaliers would be willing to sign Dellavedova for such a high price.
As beloved as Dellavedova was by James, Cavaliers' teammates, coach Tyronn Lue and team management, the Australian had a sub par playoffs and lost his back-up point guard role to veteran Mo Williams in the last two games of the finals against the Golden State Warriors.
Dellavedova did not leave the bench in the Cavaliers' decisive game seven win.
If Dellavedova does join the Bucks he will play alongside 216cm tall Australian rookie Thon Maker, selected by Milwaukee last week with the 10th pick of the draft.
The huge offer by the Bucks was just one of many announced by teams the past 24 hours as a gold rush type atmosphere to sign players overtook the league when free agency began.
A new nine-year, $US24 billion TV deal signed by the NBA has kicked in and increased team salary caps from last season's $US70 million to 2016/17's $US94 million.
The Cavaliers' appear set to let another bench player, centre Timofey Mozgov, go. Mozgov, who averaged just five minutes of court time and 1.4 points in the finals series against the Warriors, has agreed to a four-year, $US64 million deal with the Los Angeles Lakers.
In other free agent deals, Jeremy Lin, a back-up point guard who Dellavedova has often been compared to for the way he captured the basketball world's attention before flaming out, agreed to join the Brooklyn Nets on a three-year, $US36 million deal.
Shooting guard Bradley Beal agreed to a five-year $US128 million-plus maximum contract with the Washington Wizards, the Orlando Magic offered point guard DJ Augustin a four-year, $US29 million deal and Chandler Parsons agreed to go to the Memphis Grizzlies for four years and $US94 million.
Australian big man Aron Baynes' teammate at the Detroit Pistons, centre Andre Drummond, is reportedly nearing an agreement on a five-year, $US130 million deal to stay with the team, despite recording the worst free throw percentage in NBA history.
Drummond shot just 35.5 per cent of his free throws in the regular season, smashing Wilt Chamberlain's deplorable 38 per cent record set in 1967-68.
Andrew Bogut, on the final year of a three-year $US36 million contract with the Warriors, remains Australia's highest-paid NBA player.
Baynes signed a three-year, $US19.5 million contract with the Pistons while recent number one draft pick Ben Simmons will earn about $US15 million in his first three years with the Philadelphia 76ers.
-AAP
