The Wings are searching for a new boss after the 42-year-old resigned over the weekend.
National League South side Welling announced the news late last night - but confirmed he will still act in an ambassadorial role for them.
Feeney, who arrived at Park View Road in March 2022, guided the club to survival after taking over, and then a 16th place finish last season.
He released a statement saying: “With a heavy heart, I have decided to step away from Welling. I have been offered a new challenge that I just couldn’t turn down.
“My stats stand for themselves regarding the ups and downs of coming in at a difficult time to save the club. I would like to thank my players, my staff and all the fans.
“Special mention to the board and Mark Goldberg, Jerry Dolke and my great friend Andy. I want to give big mention to my friend for life, and what an honest soldier he was, in Jake Winchester who stood side by side with me through it all and for every emotion.
“And to my boss in the club who fully believed in me and was more than a boss to me. It was the most difficult decision I had to make when telling him about my decision.
“What a great man and I’m proud to call you a friend and more for life. Good luck in your next adventure. Up the Wings.”
Welling United said: “The club would like to thank Warren for all of his efforts during his time at Welling and wish him all the very best for the future.”