The 31-year-old Dubliner made a surprise switch from Kilmarnock to the capital the day before the summer transfer window shut.
Despite netting scoring 27 goals in 61 appearances for Killie, he was allowed to leave by boss Allan Johnston and chairman Michael Johnston.
The Rugby Park side have failed to win any of their five Scottish Premiership matches so far but Pat Fenlon's men have done little better, with just one victory to date.
Their season started in the blackest way possible after losing 9-0 on aggregate to Swedes Malmo in the Europa League qualifiers - the worst ever European result for a Scottish club.
But Heffernan claims that scoreline was not enough to dissuade him from moving to Edinburgh and believes there is much more to come from Hibs.
"I saw the 9-0 against Malmo but it wasn't something that put me off coming here," he said. "It was very early in the season - it was pre-season really. It's hard to judge a team on that because Malmo were a good side who are halfway through their season. It was just one of those nights were everything went for them. That can happen in football.
"But we can definitely get back to challenging for Europe. We have a squad here that is good enough to be in the top six. But there's no use saying that. You need to prove it on a Saturday."
Heffernan's place in the Kilmarnock team came under threat following the arrival of former Scotland international Kris Boyd but his lethal scoring record proves he still had plenty to offer Killie.
So the player himself admits it was quite a surprise when he was told by the two Johnstons he was free to go.
He said: "It all came out of the blue. I was at Kilmarnock and my agent spoke to the chairman, who said he was willing to let me go for free.
"My agent then spoke to Hibs and they were interested in bringing me here and that's how it happened. It was so quick. I was training as a Kilmarnock player on the Thursday and by the Friday I was having a medical at Hibs.
"That's what happens in football. When a new manager comes in, he is looking to freshen the place up a bit and that's fine. I have no problem with that.
"I hadn't spoken to Allan about leaving but maybe the chairman wanted to free up some wages to get other players in because the finances are pretty tight. That's what would have happened I would have imagined.
"But it's worked out well for me. I've signed a two-year deal at a bigger club and I'm delighted."
Hibs have struck just three league goals this season but Heffernan believes with him, new £200,000 signing James Collins, Rowan Vine - who returns alongside Liam Craig to take on their old St Johnstone team at McDiarmid Park on Saturday - and young frontman Ross Caldwell, Fenlon has more than enough striking options to see that tally improve.
He said: "We have four good strikers here now and all of us are capable of scoring goals. Whoever is in the team will have to do enough to make sure the manager can't leave them out. It's all good healthy competition.
"Even if you are only getting on for the last half an hour, you have got to impress the manager and make sure it's hard to leave you out."