The Manchester-born full-back has admitted previously that moving closer to his family was a temptation.
But he this week agreed a new three-year contract to remain at Pittodrie.
"It was definitely a big factor in me signing," the right-back said of McInnes' decision. "It was nice to re-assured that he would be the manager."
Logan, 29, joined the Scottish Premiership club from Brentford in May 2014 and had been linked with a move back to England.
"It was always a temptation," he said. "My family's down there, my friends are down there, but at the end of the day it is about enjoying football and being happy and I am more than happy here.
"Family has never been an issue. The manager gives me more than enough time to see the kiddies and I can arrange for them all to come up and spend time with their dad up here.
"So it is probably a stage of my career where I thought a three-year deal at club where I've been for three and a half years it suited me down to the ground.
"It would have been difficult signing under a manager I had never played under."
McInnes paid tribute to Logan for the way he has handled his family situation.
"Shay's not had it easy because of that," he said. "His own situation domestically is a huge commitment for him to see his kids.
"But that's another positive of Shay Logan - how committed he is to his family and his children - but at no point does he lack that commitment to us.
"He gets quality time with his kids, but he also brings us the necessary work to prepare for a game.
"He never misses training. He's consistently fit and available and he's chalked up a lot of games. He is a fantastic boy to work with."
McInnes also praised Logan's quality as a player.
"It's important that we try to retain good players, players that have served us well and there's no doubt that Shay, from day one, has impressed us all," he added.
"A lot is made of his personality, his confidence and rightly so and I think the fans are drawn to that.
"But what also has to be said is that he is a very good player and he's been voted the best right-back in the league in the last few seasons and rightly so.
"He has been a brilliant signing and I'm delighted he has shown that commitment to be with us."
Shay Logan says Derek McInnes' decision to turn down Sunderland - rather than his own family situation - persuaded him to extend his stay with Aberdeen.