Goalkeeper Lukas Lidakevicius and winger Toni Silva have left Barnsley, the Championship club have confirmed.
Lidakevicius joined Barnsley's Academy in August 2011 before turning professional ahead of last season.
But the Lithuania U21 international failed to make a first-team appearance for the Tykes.
Portuguese winger Silva moved to Oakwell from Liverpool last summer but failed to make an impression.
The 19-year-old leaves Barnsley after making only one first-team appearance.
Meanwhile, Christian Dibble has moved to Oakwell from Bury after speaking to Barnsley goalkeeper coach Ian Willcock.
"I'm obviously very pleased," Dibble said. "I was very surprised because one minute I'm signing for Bury and then suddenly I got a call off Willco saying they wanted to sign me so I'm very pleased about it."
The 30-year-old, who left North End by mutual consent last week, has put pen to paper on a two-year deal with the Shakers.
Procter joined the Lilywhites from Accrington where he made over 300 league appearances in 10 years.
His departure from Deepdale brought to an end an 18-month stint with the League One club.
Procter becomes Bury's sixth signing since the League Two outfit's transfer embargo was lifted.
Moyes swept into what is now known as the AON Training Complex at 8am on Monday morning to begin the task of succeeding the most successful manager British football has ever known.
As anticipated, shortly afterwards came confirmation that Steve Round, Chris Woods - who will remain the USA's goalkeeping coach until next year's World Cup - and Jimmy Lumsden had followed Moyes down the East Lancs Road from Everton, filling the posts vacated by Mike Phelan, Eric Steele and Rene Meulensteen since Ferguson's exit.
With an in-house TV crew in addition to the club's own photographer on hand to capture the first shots of Moyes in his new environment, it was all fairly straightforward.
Certainly there will be more challenging days ahead, starting with the planned meeting with Wayne Rooney that is likely to determine the striker's future, which will almost certainly take place on Tuesday.
But for now, Moyes is riding the crest of a wave.
"I have worked with Steve, Chris and Jimmy for a number of years and I am delighted they have decided to join me at this great club," said Moyes.
"They bring great qualities in their respective fields and I know that, like me, they feel that this is a challenge to relish.
"I have great faith that together, we can build upon the success this club has enjoyed over many years."
Moyes has been backed by executive vice-chairman Ed Woodward, who has formally assumed most of the football club responsibilities previously held by David Gill, another part of the seismic changes being felt at Old Trafford.
"I believe with David and his new team in place, along with our current backroom staff, we can now start preparing for the new season ahead," said Woodward. "This is an exciting and challenging time for the club and I have great belief that David and his team will have all the energy and attributes needed to help this club continue in its long-standing traditions."
Yet Moyes and Woodward face a tricky dilemma in their handling of Rooney.
Although it was suggested Moyes wanted Rooney to remain at United despite the England man's falling out with Ferguson at the end of last season, it seems that hope will not be realised.
It has been suggested by a source close to the impending discussions that the odds are presently "60-40" in favour of the 27-year-old ending his nine-year association with Old Trafford.
Whilst many, possibly the majority, of United fans would not be too dispirited by such an outcome, it would create the potential for additional criticism of Moyes should they fail to emerge from a tough start to the season - featuring matches against Chelsea, Liverpool and Manchester City in the first five games - with fewer points than anticipated.
Rooney and Moyes held one meeting immediately after the Scot's appointment, when it was decided further discussions were needed.
But with a formal acknowledgement that Rooney never asked for a transfer, as Sir Alex Ferguson stated after his final home game in charge against Swansea in May, a significant stumbling block to an agreement, and action required on a massive contract that only has two years remaining, it is difficult to see the striker's opinion altering significantly.
Then, Moyes would be left mulling over whether he should take Rooney on a three-week tour of the Far East and Australia given the forward will almost certainly remain a United player when they depart on July 10, even if his long-term future lies elsewhere.
It is certainly difficult to see any swift conclusion to a Rooney exit as, having been linked to Arsenal, Chelsea, Paris Saint-Germain and Barcelona already, other suitors are likely to reveal their hand once they know for certain the player has opted to move.
And that is just one conundrum facing Moyes.
Further pursuit of Leighton Baines, which would shove Patrice Evra towards the exit door, must be decided upon, whilst clarification on Thiago's intended move from Barcelona may also be required after the midfielder's cryptic weekend post on Twitter underlining his love for the Catalan giants.
With links to Benfica defender Ezequiel Garay and PSV Eindhoven midfielder Kevin Strootman to yield any concrete developments, Moyes will be given little time for a honeymoon period before proper pre-season work begins on Thursday.
