Many fans were surprised when the Magpies signed Carroll in the summer, given his injury history over the past few seasons.
The last time Carroll appeared in more than 20 Premier League games in a season was the 2015-2016 campaign for West Ham United.
He has struggled with ankle problems, while he did not score a single Premier League goal during the 2018-2019 season.
Carroll emerged on the Premier League scene with Newcastle in 2006-2007, but he took a few years to find his feet.
And Williamson, now Gateshead player-manager, thinks that given Carroll's status with the fans, his return was the type of move that can help to improve the atmosphere at the club.
In an exclusive interview with Tribal Football, Williamson said: "Yeah definitely. It's the perfect fit really. He's obviously a bit of a cult hero and a homegrown lad. I played a couple of years with him.
"He's an unbelievable player when he's fit and up to speed. He's just had a full difficult years with injuries. But it seems to be perfect timing with the fact that Newcastle could use somebody like that, a talisman that can come in and really light St. James' Park up.
"And off the back that Andy's not getting many minutes on the pitch over the last couple of years, it's the perfect time for him to come back and get himself fit and show everyone what he can do because he's a world-class striker. There's no doubt about that. So it's brilliant he's back."
Carroll's breakthrough at St. James' Park occurred during the 2010-2011 season, when he netted 11 goals in 19 league appearances.
Williamson revealed there were few hard feelings among the players when Carroll initially left Newcastle for Liverpool in a £35 million transfer in January 2011.
Many fans were furious with Carroll at the time, but Williamson says that he and the other players understood Carroll's desire to go to a club competing higher in the table.
He said: "Football's football.
"I think everyone that was there was experienced enough to know that when an opportunity like that comes up, the money that you're talking about as well, it's very difficult for anything other than him leaving.
"As a team nobody wanted to lose him but when something like that comes up for one of your friends you want them to take that opportunity and take that challenge because you really can't turn it down."