The full-back is the third senior player from the administration-hit club's first-team squad to agree a wage cut after keeper Jamie MacDonald and midfielder Ryan Stevenson also volunteered to accept a reduced salary.
Scotland Under-21 defender Kevin McHattie, meanwhile, is also close to agreeing a similar arrangement.
But former Kilmarnock player Hamill says only a sense of loyalty to the Gorgie side has stopped him moving on. He told Press Association Sport: "I've had some long discussions with the gaffer and the directors and it was a tough decision.
"But at the end of the day, Hearts have been good to me. So I'm just repaying the favour. I missed two cup finals and I want to help the club get back to that kind of level where we are competing. It was difficult choice to make but I feel like I've got unfinished business.
"I've had a few discussions with other clubs but nothing concrete. However, I decided I wanted to stay here and help Hearts."
Hearts owe £25million to Lithuanian firms Ukio Bankas and UBIG, who are also major shareholders in the club and enduring their own financial crises. UBIG are appointing their own administrators while Ukio Bankas - who have a floating charge on Tynecastle as protection for the £15million owed to them by Hearts - lost an appeal against liquidation.
Hearts were forced to appoint finance trouble-shooters BDO in a bid to stave off a winding up order set to be launched over a partially-paid £100,000 tax bill. But by calling in administrators they triggered a 15-point Scottish Premier League punishment.
BDO have already laid off 14 members of the Jambos backroom staff and say the club must sell 3,000 season tickets in the next 10 days if it is to survive.
The Hearts support who raised £1million to save the club from an earlier court bid launched by Her Majesty's Revenue and Customs have rallied to the cause once more, purchasing 1,200 since Friday. Hamill said: "The fans have been amazing. Hopefully they can keep giving us their support for the rest of the season and help us out of this situation."
- Sports & Recreation