The attacking midfielder, 26, has scored 13 goals since joining the Mariners – formerly managed by Paul Hurst – last January.
The attacker is formerly of Heanor, Alfreton and Gateshead.
He takes Town's deadline day business to three players after the additions of Abo Eisa and Nathan Thomas.
Boss Paul Hurst, who did not manage Jones at Grimsby, was delighted in getting the deal – that was confirmed after the 11pm deadline – finalised.
There had been speculation linking the goalscoring midfielder with a move to Scunthorpe.
It completes Shrews transfer window business after an exhaustive deadline day search to five new signings, alongside the earlier deals to bring in Luke Hendrie and Max Lowe.
But Hurst was keen to bolster his attacking additions late on in the window and landed long-term target Thomas as well as non-league flier Eisa.
“I’ve just drove down now, so it’s all pretty last minute, but I’m buzzing to be here," Jones said after sealing the deal.
“I heard about it at about six o’clock and that was the first I’d heard of it, so it was out of the blue. There was another option, but this was the clear option for me.
“When I got back into football about three years ago my main aim was to go as far as I can and for me this is another opportunity where I can try and show what I can do at this level now.
“I’ve done it at League Two, I’ve done it in the Conference, so hopefully I can push on and show that I can do it in League One."
Jones admitted he can play in number of positions but described himself as an attacking midfielder. He will join fellow deadline day signings Thomas and Eisa in training at Sundorne Castle tomorrow.
“I’ve played in a fair few positions to be fair," he added.
“I see myself as an attacking midfielder, but obviously I’m here to play wherever the Gaffer wants to use me, so hopefully I will just get some game time.
“I know one of the boys from Gateshead, James Bolton, but I am looking forward to meeting all the lads and hopefully joining in with what they are already doing.
“The start they’ve had to the season and the way they’ve been doing in League One is unbelievable, so for me it’s a privilege to come on board and hopefully contribute in some way."