Atkin had already signed a two-year deal with the Robins starting in 2018.
However, with on-loan Hull FC half-back Jordan Abdull absent due to a knee injury until September and Championship rivals Swinton in financial trouble, he now joins early ahead of the transfer deadline.
Having secured top spot, Rovers are seeking a return to the Super League via the Qualifiers and Hudgell said: “We’ve sorted the paperwork and it’s all agreed.
“Tim (Sheens) likes him and believes he has a little something about him. He is a bit of an unknown quantity and gives us another option.
“It doesn’t mean we’re not looking at other halves as well.
“There’s a couple of options available to us and another front-row is a possibility as well.”
Elsewhere, Salford Red Devils have made their own signing ahead of the business part of the season confirming prolific ex-Kiwi winger Manu Vatuvei on a contract until the end of 2018.
He scored 152 tries in 226 games for New Zealand Warriors and is essentially a replacement for Justin Carney who joined Hull KR in May.
Vatuvei, 31, is set to debut against Leigh Centurions on Friday week and play against Wigan Warriors in the Challenge Cup semi-finals a week later.
Salford’s Junior Sa’u faces a potential two-game ban for a reckless Grade B high tackle on Leeds Rhinos’ Kallum Watkins.
Warrington Wolves’ Ben Westwood could miss up to five games for a dangerous tackle on Leigh’s Danny Tickle.