The Premier League club beat competition from Crystal Palace as well as LaLiga side Valencia in order to secure a short-term deal for a player who has struggled for regular game time following his £40 million move from Ajax in 2020.
"Now I can say I am an Everton player, I am really happy and can't wait to help the team," Van de Beek told evertontv. "I think it is a great club... there are really good players here and I came because I want to help them go up the table.
"I hope to bring my football qualities, my passing, and, of course, scoring goals. It is a big part of my game to score and give assists and I will try to do that again. And it is not only offensive, you have to defend as a midfielder and I can do that as well.
"I had a really positive meeting with the new coach. We have the same ideas about football and he had a lot of influence on my decision.
"I played against him when I was at Ajax, and he was at Chelsea [as manager], so he knows me as a player. He thinks I have qualities that can help the team.
"I can learn a lot from him because he was a little bit in the same position - a midfield player who scored a lot of goals.
"He can help me a lot, so I think I'm in a good spot.
"I want to improve with Everton. There are always things that can be better and I work hard every day to do that."
Sources told ESPN that Everton were keen to sign the midfielder last summer, when Marcel Brands, then director of football at Goodison Park, lined up a deal to take him to the club. But, having told Van de Beek and his representatives that he could leave, then-United manager Ole Gunnar Solskjaer performed a late U-turn and insisted he wanted to keep him at Old Trafford.
But Van de Beek has struggled to feature under interim manager Ralf Rangnick following Solskjaer's dismissal and will spend the rest of the season at Everton in a bid to find regular first-team football. Sources said Rangnick was initially reluctant to sanction so many exits halfway through the season but the performances of Anthony Elanga convinced the German he would still have enough options to navigate games in the Premier League, FA Cup and Champions League.
Anthony Martial has joined Sevilla on loan while Jesse Lingard and Dean Henderson's futures still need resolving ahead of the closure of the transfer window at 11 p.m. GMT (5 p.m. ET) on Monday, Jan. 31.
In total, Van de Beek has completed 90 minutes on nine occasions for United. This season, his eight Premier League appearances have amounted to 68 minutes on the pitch, while three of his last five league games have been one-minute appearances from the bench.