The England international established himself as one of the best central defenders in the Premier League at Burnley, just two seasons after leaving United in January 2015. Keane's form had attracted interest from United and the Red Devils' manager Jose Mourinho was looking at the option of signing him.
However, the Portuguese tactician secured the services of Victor Lindelof from Benfica. Despite the Swedish international's arrival, United were still interested in signing their former player.
The 24-year-old eventually turned down the approach from United to complete a club-record £30m ($38.3m) move to Everton on 3 July. The defender, who signed a five-year deal with his new club, claims the Toffees are the best club for him to continue his development.
"Of course it was a temptation [to join Manchester United] - it's your boyhood club but you have got to take your heart out of it sometimes and think what's best for you, and I feel as if this is the best place for me to come and continue my development," Keane told Sky Sports.
"It's a club with such big history and a great fan base so I can't wait to pull on the shirt and play for this club."
Keane also stressed on the role that Everton manager Ronald Koeman and club chairman Bill Kenwright played in him joining the Merseyside club.
"He [Koeman] used to play in my position. I have been fortunate enough that in the clubs I have played in the past, the manager has played in my position as well and I feel like he was a very classy centre-half. So he can still teach me things," the defender explained.
"I want to develop, I am only 24 years old, which is young for a centre-half but I feel how much they wanted me was a big factor as well.
"Bill Kenwright has got a great relationship with my representatives and he was a major factor in me coming here, and Steve Walsh as well. I know him from my days at Leicester [City], so I felt really wanted by everyone at the club and I just can't wait to get going now."