Long-serving manager Parker continues an association with the Hallmark Security League (formerly North West Counties League) club, which began as a player more than 20 years ago.
Another stalwart servant of the Mechanics Ground club, Tommy Baldwin, becomes vice-chairman, while Parker’s former assistant manager Alan Williams has moved on.
Club spokesman Neil Carman paid tribute to Parker, saying: “There surely can’t be many managers who stepped up from playing for a club and then eventually climbed to the top of the ladder as club chairman.”
New boss Worthington has a thorough knowledge of the local football scene from his time as player and manager of Blackpool Wren Rovers.
He brought silverware to the Bruce Park club, including Wrens’ first league and cup double for 40 years in the 2009-10 season.
Worthington has already drawn up a list of potential signings and is assembling a backroom team. Martin Baird has been confirmed as player-coach.
The new manager said: “I’ve always wanted to step up to the next level and I was delighted when I was asked to come in as the new manager at AFC.
“Initially I want to get to know the club and the current players, and obviously they’ll need to get to know me.
“There are a few who I am looking to bring in, not drastic changes initially but it would be good to freshen things up a little bit too.
“I am really glad that Stuart is staying involved. He has been a real stalwart of this club for many years and I can tap into his vast knowledge and experience around this league.”
The Jepson Way club was in danger of dropping out of the Hallmark Security League last season, finishing two places above the first division relegation zone as they again struggled after falling out of the premier division the previous season.