The 24-year-old has moved to Merseyside, becoming the club's second signing of the January transfer window following Landon Donovan's loan move from Los Angeles Galaxy.
The midfielder, a product of the United youth team, scored 10 goals in 60 appearances for the Old Trafford side since breaking into the first team in the 2005-06 season.
Gibson, who was born in Northern Ireland but opted to play for the Republic of Ireland, has played 17 times for his country, scoring once.
Reports suggest the initial fee for Gibson is £1million with a further £1million appearance-related.
"I can see a hunger," manager David Moyes told the club's website.
"He (Darron) is young and wants to prove himself," .
The Ireland international is unlikely to be the last arrival at Everton this month with the Toffees boss looking to strengthen in central defence and up front.
However, the Scot has said he may have to look to loans to fill gaps in certain areas.
Some advice from Manchester United team-mate and former Toffees striker Wayne Rooney helped convince Gibson to move to Goodison Park.
Frustration at not getting first-team chances at Old Trafford played a significant part but the 24-year-old said after speaking to the England international - and then Everton duo Phil Neville and Tim Cahill - his mind was made up.
"I was speaking to Wayne about it a bit and after that and coming to see the facilities it was an easy decision," Gibson, who is in the squad to face Aston Villa on Saturday, said.
"He told me it was a great club and he really enjoyed his time and the people here.
"Having a word with him and people like Tim Cahill and Phil Neville convinced me to come."
Gibson knew he had little future at Old Trafford when Sir Alex Ferguson decided to bring Paul Scholes out of retirement.
The 37-year-old, who quit the game last season, was brought back on a short-term deal to provide cover for an injury-stricken midfield and came off the bench in last weekend's 3-2 FA Cup third round victory at Manchester City.
"I was very frustrated [at Manchester United]. It was hard for me at times," the Republic of Ireland international added.
"I think when I did get a chance I did well and obviously I was getting left out afterwards and I was playing one or two games here and there.
"When Scholesy came back the manager told me I was free to go.
"Everton had shown some interest a month before hand and the gaffer (David Moyes) wanted me in so it went from there.
"It was very frustrating but I think it was the right time for me to move on and I'm looking forward to my time here.
"I'm really looking forward to kicking on now.
"When everyone's fit it's a great squad and hopefully me coming in can improve the team a bit and we'll start to kick on from here.
"I have been at United since I was 15 so this is the first proper move I have had so it is very exciting.
"David Moyes is a great manager and has shown that over the past few years.
"His teams have been good despite not having a lot of money so I'm really looking forward to working under him."
Gibson is known for being able to find the net and work the goalkeeper and that is something Everton are crying out for, but he hopes to be able to offer other qualities to the side too.
"I have not had a run of games properly so when I get into the swing of things I can bring a lot of things," he said.
"It's a great club with great fans and hopefully I can improve Everton.
"I think I'm a goalscoring midfielder and hopefully I can get a few goals.
"I've scored a few long-range shots - I don't think I've scored one inside the box to be honest - and if I score goals it's a bonus for me.
"I'm just looking to do as well as I can for the team."
Gibson also hopes the chance of more regular football will improve his international opportunities, especially with Euro 2012 on the horizon this summer.
"I wasn't playing at United which meant it was hard for the international manger (Giovanni Trapattoni) to pick me," he added.
"But once I start playing here hopefully he'll have no choice but to pick me."
