This will open tomorrow at the end of a week during which they have been hit by a transfer embargo for failing to pay their players on time.
Hearts claim that, if fully subscribed, the share offer could raise up to £1.79million with supporters taking control of 10 per cent of the club's shares.
Club director Sergejus Fedotovas believes the offer could lead to supporter ownership in future.
He said on www.heartsfc.co.uk: "It is a very important moment in Hearts' history where supporters are invited to secure the club's future.
"Hearts needs its supporters more than ever and we count on this appeal being heard and supported.
"If this first share offer is successful we believe future proposals could be considered that may eventually allow for Hearts supporters to take over the club.
"Every pound raised by supporters, after costs, will be reinvested into the club. We expect this will be a popular offer."
Hearts were this week issued with a player registration embargo of 60 days, until December 23, by the Scottish Premier League after admitting to failing to pay all of their players and staff on schedule for September and October.
Finances have been tight at Tynecastle since majority shareholder Vladimir Romanov said he was disillusioned with football and four times last season wages were delivered late.
The share offer opens tomorrow morning, ahead of the home SPL clash with Ross County and revenue will be used "in meeting general working capital requirements".