Saunders has left Wrexham after three years to succeed Sean O'Driscoll at Doncaster Rovers.
Morrell will be in charge for Saturday's Blue Square Bet Premier game at Grimsby.
"I spoke to the directors on arriving at Colliers Park this morning and they have asked if I would take on the first team affairs," said Morrell.
Doncaster-born Morrell is in his second spell at the Racecourse after being re-signed by Saunders in June 2010.
The 35-year-old had originally joined the north Wales club from non-league side Newcastle Blue Star in 1998.
Morrell left the Racecourse to join Coventry City on a free transfer in 2003 before spells with Blackpool and Bury.
"I'm only too happy to help out," Morrell told Wrexham's official website.
"It's come a little bit earlier than I was planning but you can't turn down such an opportunity, they don't arise too often
"I feel I still have plenty to offer as a player and this will also allow me to see what life is like on the other side of the fence."
Morrell will be assisted by coaches Brian Carey and Michael Oakes for Saturday's trip to Grimsby Town.
Morrell scored a record seven goals for Wrexham in a FAW Premier Cup tie against Merthyr Tydfil
Saunders succeeded Brian Little as Dragons boss in October 2008 but Morrell said the job at Doncaster was one which the former Wales striker could not refuse.
"Personally I can only wish him well at Doncaster and thank him for all the help he has given me," said Morrell.
"But it's fantastic for him to get such an opportunity and it also reflects well on our club. "
Wrexham have put striker Andy Morrell in temporary charge following the departure of Dean Saunders.