Simpson, 31, who is valued at around pounds 75,000, will go straight into the squad for tomorrow's West Midlands derby with Birmingham City at St Andrew's.
The former Manchester City and Oxford United player has been out of the first-team picture at Pride Park this season, but has impressed McGhee in the reserves.
"They don't want a lot of money for him and what I said to the boy is that I don't want him here if all he is going to do is clutter up the place by not being in the team," the Wolves manager said. "But, if he comes and proves he can make a contribution this season, then he can stay and he is up for the challenge. He wants to play first-team football."
The Welsh international defender Adrian Williams has returned to Molineux after being pulled out of the World Cup qualifier with Belgium because of an Achilles injury.
The Bolton manager Colin Todd has denied reports that the midfielder, Jamie Pollock, has asked to go on the transfer list. "The situation is that Jamie has been doing a job for the team and has been asked to play out of position," Todd said. "I have been playing him wide on the right, whereas his favourite position is in central midfield, where I have not been able to accommodate him so far.
"The player is disappointed and unhappy, but we've talked it through and I've agreed that, if an offer comes along that is right for the club and the player, then we will listen to it."
Pollock, 23, a former England Under-21 international, joined Bolton for pounds 1m just under a year ago from the Spanish outfit Osasuna, after first making his name with Middlesbrough.
The Manchester City manager Frank Clarke is facing a selection crisis after hearing that Uwe Rosler has been ruled out of action for six weeks. Clarke may be forced to buy a replacement for the German forward, who damaged ankle ligaments in a friendly with an Italian select XI this week.
The transfer-listed Rosler will not be available again until late November, which will also put an end to his chance of a move to Everton.
Rosler's lay-off leaves City short of bodies. There are fears for Paul Dickov, who went to hospital for a scan on his knee yesterday after picking up an injury in the same game.
Dickov could need a minor operation, and that would leave City with just their record signing Lee Bradbury in attack as they try to escape the bottom half of the First Division.
The West Bromwich Albion striker Paul Peschisolido has rejected an improved contract with the Hawthorns club. He had said earlier in the week that he was "very close" to signing a two-year extension to his current deal, which has 18 months to run. Then talks broke down, with the Canadian international and Albion unable to reach agreement. The 26-year-old insisted: "I won't be signing a new deal."
Peschisolido, who dropped his agent Eric Hall from the talks after he was involved in a row with Albion's chief executive, John Wile, said: "I met with chairman Tony Hale but we could not reach agreement."Reuse content