Ray Allen was in tears the last time he visited AmericanAirlines Arena, his Boston Celtics having been ousted by the Heat in the deciding game of the Eastern Conference finals.

When he returned last Thursday to hear the Heat’s recruiting pitch, Allen felt a comfort level and connection — the type of feelings Heat president Pat Riley routinely seems to engender when he meets with free agents.

“Pat’s a guy after my own heart,” Allen said Wednesday, the first day NBA rules allowed him to make official his move from Boston to Miami. “Very disarming guy. We talked over the course of that day for four or five hours” — covering topics ranging from basketball philosophy to books to movies.

“The next day, he texted me some good quotes. I really liked that.”

But it wasn’t only Riley that left an impression. Coach Erik Spoelstra did his part, too.

“We shared very similar ideals, offensively, defensively,” Allen said. “We talked about every basketball philosophy we shared, to the point where he said, ‘I don’t know if you’re coming, but I’ll tell you this anyway.’ ”

LeBron James and Dwyane Wade lobbied him with text messages, though Allen said that carried more weight with his loved ones than with him.

Allen returned home to Connecticut on Friday, very interested in the Heat but still undecided whether to leave the Celtics after five years.

“I’m thinking about, ‘Is Miami going to be a good fit for me?’ ” he said. “I talked to the people around me that have watched me, and they just said, ‘Change is not bad. You have to consider this.’ It was that moment where we said this is going to be a great opportunity for me. I was excited.”

Excited to the point that he took a two-year deal from Miami at slightly more than half the value of the two-year, $12 million contract offered by Boston. Also signing Wednesday was Rashard Lewis, who gets a two-year, $2.8 million deal.

Allen said he wasn’t sure if there was anything Boston could have done to keep him.

“We have added probably one of the most professional professionals this league has ever seen,” Riley said.

Asked about coming off the bench behind Wade, Allen joked, “You mean I’m not starting? Wish you had told me that last week.”

‘Big’ role for Allen

The NBA’s all-time leader in three-point baskets, Allen said starting “wasn’t really an issue. Whatever is going to be best for me in this situation is going to figure itself out. This team won a championship without me. I’m not going to come in and expect for coach to cater to who I am or what I do.

“I’m not trying to come here and win on my terms. Whether you start or come off the bench, the best compliment is who you finish the game up with.”

Spoelstra declined to specify Allen’s role beyond saying it will be “big. We want to get to a point where we are position-less. He’s a great complement to the champions we have.

“There are only a handful of players in this league that absolutely strike fear into their opponent. And Ray is one of those players. Hopefully, we can play faster.”

Allen, who turns 37 on July 20, found the Heat’s style especially appealing.

“I’m ecstatic Rashard Lewis is here because this is similar to how we played in Seattle: spread the floor, attack, get to the basket, make the easy extra pass,” he said. “That’s what Miami did to us the last couple years.