Round previously spent six seasons with the club, scoring 53 goals in 251 appearances.
Capable of operating as both a winger and wing-back down the left, the 28-year-old was part of the club's promotion-winning squad of 2021/22.
Round would go on to make the move to the National League North last season, joining Blyth Spartans in November 2022.
He has already trained with his new team-mates ahead of Saturday's league game at Matlock Town.
It will be an important game for the Seasiders, who have won just one of their opening six Northern Premier League fixtures, losing the other five.
Manager Graeme Lee said: "I'm delighted to sign Curtis. He's a player well-known to the club, and it’s fantastic to get him back.
"Curtis will be a great addition to the squad. He is a very good player, but also has the experience and character we are looking for."
Photo credit: Marske United