Moyes will take over from Alex Ferguson in the Manchester United hotseat on July 1.
And one of his first targets will be a £15million move for England left-back Baines — with the prospect of making it a £39m double swoop for Fellaini too.
Moyes, 50, stays in charge at Everton for the last two games of this season.
And the Scot will bid an emotional farewell to Goodison Park in their final home game of the season against West Ham on Sunday.
Former Wigan full-back Baines, 28, has long been on United’s radar but the champions have never made an official approach.
That is set to change when Moyes checks in with the mouthwatering bonus of having the attack-minded Baines providing ammunition for Robin Van Persie in the middle.
Everton know they are powerless to stop him the soon-to-leave manager moving for the defender, who is already odds-on to start next term at United.
And they are equally aware it would be hard to deny a player such a move — the chance to join one of the biggest clubs in world football.
United also need to strengthen the midfield, and a £24m release clause in Fellaini’s contract means the fee is already public.
The fact Fellaini, 25, can play as an attacking midfielder or an enforcer — something United have lacked in recent years — makes him doubly appealing.
And the Belgian has openly admitted he wants to play in the Champions League.
Moyes’ appointment at United means Fergie has got his man 15 years after first trying — and sees the departing boss getting his way for one final time.
Ferguson told Old Trafford top brass — who originally feared Moyes was not a big enough name and would affect the share price — he was his overwhelming recommendation to replace him.
He first tried to tempt his fellow Scot to United as his right-hand man in 1998, when Moyes was still chasing Championship promotion as Preston boss.
And after imposing his will on the 20-time champions as his parting gift, Fergie admitted: “When we discussed candidates we felt had the right attributes, we unanimously agreed on David.
“I’ve admired his work for a long time and approached him as far back as 1998 to discuss the position of assistant manager here.
“There is no question he has all the qualities we expect of a manager at this club.”
Fergie’s decision to retire was such a bolt from the blue that Moyes only learned of United’s interest last Thursday.
Two days earlier he was still working on Everton’s plans for next pre-season.
Yet, after being handed a six-year deal at Old Trafford, he admitted he was “thrilled and delighted” by his appointment.
Moyes confessed: “It’s a great honour and I’m delighted Sir Alex saw fit to recommend me for the job.
“I know how hard it will be to follow the best manager ever.
“I have had a terrific job at Everton, with a tre-mendous chairman and board and a great set of players. Everton will be close to me for the rest of my life.”
The news the world was waiting for finally became official in mid-afternoon, when both clubs released statements — Everton's pipping United by a few minutes.
The Blues confirmed: “David Moyes will leave at the end of the season.
“He met chairman Bill Kenwright and confirmed his desire to join Manchester United.
“Everton officials will start the search for a replacement immediately.”
That followed an embarrassing false start by United, whose Facebook page had earlier put up a picture welcoming Moyes to Old Trafford.
Bookies reacted to Moyes’ appointment by making United 15-8 SECOND favourites to retain the title, behind Manchester City.
But the new manager’s teenage daughter has no doubts that her dad will be a smash hit.
Lauren Moyes tweeted: “Ferguson has been a wonderful manager for Manchester United and my Dad will continue his success.” The Sun