The Miami Heat have scored another free-agent coup, convincing Ray Allen to leave a richer offer from the Boston Celtics and agree to sign with the defending champions, agent Jim Tanner told ESPN.com.

The Heat felt positive about the presentation they made to Allen over several hours in a meeting on Thursday in Miami, sources said, but Allen flew back to his home in Connecticut to mull over the decision. He informed both teams Friday night of his decision.

It is believed Allen will accept the Heat's mid-level exception that starts at $3.09 million and could be worth a maximum of $9.5 million over three seasons.

"#HeatNation please welcome our newest teammate Ray Allen #Wow #JesusShuttlesworth," LeBron James tweeted Friday night.

Boston, where Allen had played for the past five seasons and won a championship in 2008, had offered Allen a two-year deal at double the salary for $12 million plus a no-trade clause. The Boston Herald reported Allen was seeking a three-year, $27 million deal.

Heat owner Micky Arison celebrated the news by tweeting, "Its 2:30am in London and I was just woken up with great news. Welcome to the family #20."

A person briefed on details of the decision told The Associated Press that Arison got the word from Heat president Pat Riley, who made Allen the team's top free-agent priority -- especially in recent days. Allen, who will be 37 this month, arrived in Miami on Thursday for a visit, went to dinner with Riley, coach Erik Spoelstra, team executive Alonzo Mourning and others Thursday night, then left Friday to presumably decide his future.

Hours later, the choice was made. Allen's agent, James Tanner, confirmed the decision to The Associated Press not long after Arison's tweet.

Allen cannot officially sign until Wednesday because of the league's moratorium.

According to multiple league sources, Allen had become frustrated during last season when the Celtics offered him up in trade talks and then stripped him of his starting job in favor of the younger Avery Bradley. Allen, who averaged 11.9 points and shot 35 percent on 3-pointers in the Eastern Conference finals loss to the Heat, also had a deteriorating relationship with point guard Rajon Rondo.