"I spent three years on it, a year-and-a-half [working] very intensely. There were many conversations with [Messi's father and agent] Jorge. [Inter Miami co-owner] David [Beckham] talked to Leo, only about football issues, because he was a player."
Messi, 36, had initially considered a return to Barca, the club he had left in 2021 due to its financial crisis, while he also rejected a lucrative deal from Saudi Arabia's PIF fund to join Al-Hilal.
"I saw it as done at the end of May," Mas said. "I didn't want him to feel under pressure. We had spoken in Barcelona, Miami, Rosario, Doha ... I spent the whole World Cup in Qatar, watching Argentina.
"The Apple contract was very important to close the deal."
MLS broadcast partner Apple recently announced a four-part docuseries on AppleTV+ about Messi's World Cup journey, from his first tournament appearance in 2006 to eventual trophy in 2022.
Messi, who is on holiday, is expected to sign a contract with Inter Miami until December 2025, with an option year for 2026, while Mas confirmed the forward will earn "between £50 million and $60m per year."
Mas also confirmed long-standing interest in surrounding Messi with players he is familiar with, including Sergio Busquets and Jordi Alba. He also said Miami will make "two or three" further signings but played down reports that two of Messi's close friends -- former Barca forward Luis Suarez and Argentina winger Angel Di Maria -- could arrive this summer.
"He [Suarez] is under contract, he has a clause, and I don't know if this will materialise," Mas said. "We have also spoken to Di Maria but it seems that he is about to sign for another team."
Meanwhile, Barcelona president Joan Laporta said Messi did not want to return to the club because he "wanted less pressure."
"I understand it, but one thing has nothing to do with the other," Laporta told Spanish newspaper La Vanguardia.
"We had an agreement with LaLiga that we would dedicate part of the resources we have to Messi. It was included in the viability plan. We communicated it to Jorge Messi. He told me that Leo had had a very difficult year in Paris and that he wanted less pressure. With our option, he would have continued to be under pressure, and I understood his decision."