Messi ended a 21-year association with Barca in August when it was announced he would not be re-signing for the club.
His contract had officially expired at the end of June but Barca and Messi were expecting to be able to announce a new deal on a reduced salary.
But even with the reduced terms, Barca was still unable to get its wage expenditure under its LaLiga-imposed salary cap, which prevented it registering new signings.
As such, Messi was officially a free agent and PSG quickly swooped to bring him in, with the Ligue 1 champion and Manchester City both being linked with him extensively in the past.
The situation surrounding Messi's inability to re-sign for Barca and his move to PSG shocked the world of football, including those at PSG.
"Messi was convinced to stay at Barcelona," Leonardo said. "We had some contacts. Some rumours were saying he may not stay at Barcelona because his contract was expiring.
"We checked the situation, we talked but we did not have the feeling he wanted to leave Barcelona. However we started networking. This helped us to be in a good position.
"Then Barcelona announced the end of their relationship, so that's the moment we started and it's been great. It's been a surprise for everybody.
"Then he arrived. The way he arrived… he was at Barcelona for 21 years. It was the first transfer he'd done.
"It was a new thing for him to be in a new dressing room. He's got an impacting silence, he doesn't talk much but he is someone to admire."
Another high-profile player signed by PSG on a free transfer in pre-season was Gianluigi Donnarumma, who departed Milan after running his contract down.
Many in Italy have been intensely critical of Donnarumma for opting to leave for the greater riches on offer in Paris, but Leonardo insisted PSG did not get in touch with him until June, two months after his exit was confirmed.
"I know it's a difficult situation," Leonardo said. "We never contacted Donnarumma before June. I don't want to be wrong, I think Milan announced in April that they were not extending the contract [of Donnarumma].
"They signed a new goalkeeper in Mike Maignan, so Donnarumma was free for the market. We had never contacted Donnarumma before, then some things happened.
"I had been in Milan but his future was not decided yet. He was free in June. We talked and we took this decision.
"We had never done previous work to have him for free. He was going to another team if it wasn't PSG. He wouldn't have stayed at Milan."