Stanley sprung a major surprise last Friday when they signed the once-capped former England, Everton and Arsenal striker until the end of the season.
But Jeffers insists the move is a natural fit and feels it has been on the cards for some time, citing friendships with former management team John Coleman and Jimmy Bell, plus current boss Leam Richardson.
"I've always had a bit of a relationship with Accrington, even as far back as three or four years ago and my time at Blackburn," he told the club's official website. "I always came to watch because a lot of my mates have always played here.
"I've kept my eye out for them and it's strange because I always felt I'd play here at some time. You get those feelings that you will end up playing for a team.
"I never saw Jimmy and John leaving so I always thought that towards the end of my career I'd end up playing for them. But they've moved on and Leam's in charge, but I'm here now anyway."