The 30-year-old, who was in the Evostik North Team of the Year at the end of last season with his 18 goals, was signed by Barrow in the summer, but has not had much game time there and has now agreed terms to return to the Seagulls under the management duo of Craig Hogg and assistant Neil Coverley.
Hogg said: "It was clear that a number of parties were interested in him after leaving Barrow recently, but after speaking to him over the past week, he expressed an interest in returning and was very excited with what the management team are trying to achieve.
"We are delighted we've been able to agree terms with him.
"Astley has been a good player for the Bay and made the Evostik North Team of the Year last season during his last spell with us, producing a good goal scoring return along the way, and we hope he can replicate that form again for us.
"He will offer further competition for places, but the young squad we have here have done very well and everyone here knows full well we must work hard and perform to high standards on a regular basis."
Mulholland, who has previously been with Ashton United, Altrincham, FC United, Chorley and Glossop, will be available for selection once International clearance comes through from the FA of Wales.
He said: "I know Hoggy and Covs and the lads still here from last season and was happy here, so that was a big factor in my decision."