Zielonka played for the Trawlerboys during the 2014/2015 season but after joining the club late, he struggled for fitness and was restricted to a few substitute appearances before being allowed to link up with Kings Lynn later on in the season.
The 29-year-old Polish forward was a fans favourite in North Norfolk and played over 100 games for the Linnets during his time there. Zielonka is comfortable playing in a number of positions, from the striker position to the wings and further back in midfield.
Having convinced the attacker to return to Suffolk, manager Ady Gallagher said: "I'm really pleased that Jacek has decided to rejoin us. It unfortunately didn't work out for him last time but after being really successful at Kings Lynn; I am delighted to have him back here. He'll give you 100% commitment, he's a very professional and fit lad who is versatile in a number of positions too. I'm confident Jacek will contribute for us in all areas this season."