And a day earlier Biarritz Olympique and Toulon will go head-to-head in the Amlin Challenge Cup final at the Twickenham Stoop (kick-off 8pm) to get ERC's unique festival of European club rugby under way.
There are only a few hundred Heineken Cup final tickets remaining of the 55,000 tickets made available for public sale.
Tickets are available from www.ticketmaster.co.uk/heinekencupfinal or call UK - 0044 844 847 1530 - or International - 0044 208 616 5111.
Both of the finalists will receive an allocation of 7,500 tickets for their own supporters. Details of of their ticket distribution policies are as follows:
Ulster Rugby Allocation -
Tickets will be available on the following dates -
Partners and Staff: Tuesday, May 1
Existing Season Ticket Holders: Tuesday, May 1 from 9am to 5pm at Ravenhill (four per Season Ticket holder)
New Season Ticket Holders: Wednesday, May 2 from 9am to 5pm at Ravenhill online (four per Season Ticket holder)
Affiliated Clubs: Thursday, May 3 from 9am to 5pm
Public Sale: http://www.ulsterrugby.com from Friday, May 4 at 5pm to Monday, 7 May
Leinster Rugby Allocation -
Season Ticket holders and Supporters Club should log into their Season Ticket account before 5pm on Tuesday, enter their payment details and the number of tickets required (maximum four per person). The lottery will on Tuesday, May 1 at 5pm.
Queries to the Ticket Office on (01) 2693224 from 9am to 5pm, Monday to Friday.
Affiliated Clubs: Approximately 2,500 tickets will be distributed internally via the club network, staff, squad and committees.
Public Sale: Leinster do not envisage any sale to the general public, but may consider this option if Season Ticket holders have been facilitated.
Ticket Prices -
2012 Heineken Cup Final: Ticket Prices £35*, £45*, £60, £75 & Group Offer 4 person ticket for £100.00* (*Public allocation at these prices currently sold out).
Fans can also buy a ticket for both the Heineken Cup and Amlin Challenge Cup finals and avail of a £10 discount on a £35 Amlin Challenge Cup final ticket. Amlin Challenge Cup final tickets start from £25, with a group offer of 4 for £80.
Meanwhile, on the Twickenham pitch, Leinster will be bidding to win an unprecedented three Heineken Cup titles in four years and become only the second side to win back-to-back titles.
Leicester Tigers (2001 and 2002) are the only club so far to successfully defend their European crown.
For their part Ulster, the 1999 champions, will be bidding to become only the sixth team to win two or more titles in what will be the fifth one-nation final - but the first all-Irish final. There have been three all-French finals and one all-English decider.
And the all-Irish final means Ireland will have an additional place in the 2012/13 tournament with Connacht joining Leinster, Munster and Ulster.