Holloway has been chasing the 20-year-old since United's Carling Cup defeat to Coventry City last month.
The Pilgrims boss told the club's official website: "I think he brings something we haven't got. He likes to run with it. He likes to take people on, right side or left side or even up front.
"He's chosen us over other Championship sides, supposedly bigger and better than us, so this myth about coming to Plymouth - we're gradually smashing that with a mallet.
"He's a fresh, young talent who wants to learn and wants to get some first-team experience, and he chose us over three other Championship sides where, in the past, I'm sure he'd have gone."
Martin has made two Carling Cup appearances for United and also played ten matches for Rangers during a loan spell at Ibrox last term.
He spent the second half of last season on loan with Stoke City, making 14 first-team appearances for Tony Pulis' side.