Finnigan, 24, is a versatile outside back who can play on either wing and also at full-back.
The Ireland representative made only 14 appearances in 2013 as he found opportunities limited with the Eagles, and he even spent time on loan at Dewsbury.
Finnigan previously came through the ranks at Bradford in 2010, but left in search of regular first-team action only a year later. From there he joined Sheffield and in three seasons made over 50 appearances, scoring 23 tries.
After the Grand Final the Bulldogs also confirmed the departure of the following nine players:
Batley Chief Executive Paul Harrison commented: “We would like to wish all our departing players well in their future careers, and to thank them all for their magnificent contribution to a truly memorable season for the club.
“I would like to assure all our supporters that everyone at the club has been, and continues, working very hard to ensure that our recruitment for 2014 will allow the club to continue the amazing progress they have shown in recent seasons.”