Saunders, who was invited in by Wrexham FC owner Geoff Moss to watch all the Wrexham players in a training match at The Racecourse on Tuesday, accepted the job at 5pm yesterday.
He said: "This is a massive step for me. I won't rest until I see Wrexham back in the Football League.
"We must aim to be in the play-offs at the very least come the end of the season."
Saunders immediately stamped his authority by calling all the players in for a double training session today.
He will be officially unveiled at a Press Conference at The Colliers Park training ground at 4pm today.
Reds owner Moss will allow the former Liverpool star to combine both roles and says the details of his contract at Wrexham have yet to be ironed out.
An ecstatic Moss, speaking on his way to the Colliers' Park training ground at 8.30 this morning said: "What a coup. What a coup for Wrexham Football Club.
"I have never met a man with so much enthusiasm. He lives and breathes football and he is so excited about taking up this job at Wrexham.
"Just to get him to agree to being Wrexham manager is amazing. He has turned down decent offers and although he will combine his role with the Welsh FA, he will only miss three Wrexham matches this season."
Saunders, who is 44, will take charge of his first Wrexham game at Forest Green Rovers on Saturday. He will be assisted by Brian Carey and Joey Jones after caretaker boss Martin Foyle was shown the door yesterday.
Saunders is Wrexham's fourth manager in 22 months and follows ex-Aston Villa chief Brian Little, who left the club by mutual consent last Saturday.
"Because the deal was only done last night, we haven't really sorted out the terms of his contract," added Moss.
"The energy and the enthusiasm Dean shows is tremendous and I've got the say that this is a fantastic appointment. It's a big risk for Dean to come down to this level but he lives in Cheshire and he has great ambitions for this club.
"I spoke to three close friends last night and they couldn't believe I've pulled it off. My sons both texted me and just used one word to describe the appointment – class.
"We've had a lot of applications but Dean was the one. We've had an horrendous couple of seasons and now it's time to put things right.
"These are exciting times for the football club."
Saunders has coached at Wrexham before, training the club's youngsters, but now he gets the chance to manage on is own for the first time in an illustrious career.
Saunders was one of the Welsh national side's most prolific goalscorers after making his Welsh debut as a 21-year-old against the Republic of Ireland in 1986.
He was capped 75 times and scored a creditable 22 goals, putting him fourth on the all time Wales list behind Ian Rush, Ivor Allchurch and Trevor Ford.
Saunders' club career is best remembered for his time at Aston Villa and Liverpool, who paid a then English record fee of £2.9million as Ian Rush's new strike-partner following the departures of David Speedie and Peter Beardsley.
In 1991-92, Saunders partnered Ian Rush in a formidable strike-force which saw the club win the FA Cup for the fifth time in its history in manager Graeme Souness's first full season in charge.
In September 1992, Saunders was transferred to Aston Villa for £2.5million and was an instant hit with the Villa Park faithful.
He developed a partnership with Dalian Atkinson and scored twice in the League Cup final to secure victory over Manchester United at Wembley in 1994.
As part of new Villa manager Brian Little's rebuilding programme, which resulted in most of the Ron Atkinson era of players being sold, Saunders was off-loaded to Turkish club Galatasaray and old Liverpool manager Graeme Souness.
He became a coach at Bradford after his retirement in 2001, and then moved to Newcastle United in 2004, initially as strikers coach, and then first-team coach, once again under old boss Graeme Souness.
In June 2007, Saunders was appointed assistant manager of Wales alongside Roy Evans.
Both Saunders and Evans were at The Racecourse on Tuesday alongside club president and former manager, Arfon Griffiths.
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