"Once LeBron signed there, LeBron started recruiting him," said Herb Rudoy, Ilgauskas' agent, according to the South Florida Sun-Sentinel, which first reported the move.
The veteran center, who started playing for Cleveland in 1997 and has never suited up for another NBA team, expects to sign a two-year contract with the Heat later this week, Rudoy said Tuesday. The two-year deal would come with a player option for the second season, Rudoy said.
"We've agreed to agree," Rudoy said.
Playing with James again was a major factor in Ilgauskas' decision.
"LeBron was very encouraging and explained the whole situation," Ilgauskas told the Sun-Sentinel. "And, obviously, he's my friend, and him being there made it a lot easier to choose."
On his Twitter feed, James quickly welcomed Ilgauskas to Miami.
"Glad u are joining me in South Beach my friend. Also thanks for the encouraging words big fella," James wrote.
The Heat had no immediate comment. They had talks about acquiring Ilgauskas when he was available this past season after being dealt in a three-team trade to Washington. The Wizards subsequently bought out his contract and made him a free agent.
Ilgauskas is the Cavs' career leader in games played, blocked shots and rebounds. The 7-foot-3 Lithuanian was drafted by the club in 1996 and overcame serious foot injuries that nearly ended his career.
Veteran forward Juwan Howard, 37, is also finalizing a minimum-scale deal to join the Heat, according to the Sun-Sentinel.
"Juwan wants to get a ring and he has great respect for Coach [Pat] Riley," agent David Falk told the Sun-Sentinel. "We've talked to the Heat. There's a mutual interest. That's all I feel comfortable saying at this point."
Howard made 27 starts in 73 games with the Portland Trail Blazers this past season, averaging 6.0 points, 4.6 rebounds and 2.4 assists while shooting 50.4 percent from the field.
They are just the latest names to join what shapes up as a serious title contender in Miami, joining not only James but Dwyane Wade, Chris Bosh, Udonis Haslem and Mike Miller, who agreed to a deal late last week that remains unsigned.
Ilgauskas told Cavs owner Dan Gilbert and general manager Chris Grant the news on Tuesday. James played a role in luring Ilgauskas to Miami, and other teams were interested as well.
"His best chance to win a championship would be in Miami," Rudoy said.
Ilgauskas was immensely popular in Cleveland, and expects to keep a home in the city.
"It's hard," Rudoy said. "It's been 14 years. It was very hard for him. I know that. When he called Chris Grant and Dan Gilbert today, it was definitely a hard decision at this stage of his career. But he wants to win a championship. That's how he made this decision."
Playing as a reserve for the first time, Ilgauskas averaged 7.4 points and 5.4 rebounds last season. For his career, Ilgauskas has averaged 13.8 points and 7.7 rebounds, and has played in two All-Star Games.
Information from The Associated Press was used in this report.