The League Two outfit have been desperate to bolster their strikeforce after star man Mullin punctured a lung against Manchester United in pre-season.
It has kept the Welshman out for over a month now and there is no specific timeframe on his return.
Wrexham were desperate to sign Luke Armstrong from Harrogate Town but a deadline day move fell through when time expired.
Town had announced Armstrong's departure but after the clock ticked past 11pm on Friday night, the paperwork had not been signed off from Wrexham's end.
The bungled transfer saw the Dragons apologise to their divisional rivals while they decided against appealing to the EFL.
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However, Wrexham have since signed free agent Fletcher, whose contract at Dundee United expired in June.
The 36-year-old has plenty of experience and has operated in the Premier League for many of his years as a professional.
The former Scotland international signed for Burnley for a club record £3million in 2009 before subsequent moves to Wolves and Sunderland, as well as a loan stint at Marseille.
"Hopefully I can bring a lot of experience," said Fletcher. "I'm 36, I'm still fit and still raring to go.
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"One of the biggest selling points was the ambition of the club, and if I can help with that then great.
"I don't think you cannot see what has been happening at Wrexham - it's been a great experience for the fans, players and owners so hopefully we can continue that."
Wrexham currently sit 13th in League Two and face Doncaster Rovers on Saturday.
And manager Phil Parkinson was over the moon to land a striker ahead of what could be a lengthy lay-off for Mullin.
He said: "I'm really pleased with the addition of Steve to the squad.
"He's missed football through pre-season, but he's trained today with the lads and it's good to have him on board.
"His pedigree speaks for itself, and he's played most of his career at a very high level.
"He's an excellent professional and that's really important to fit in with the group here."