The Heineken Cup (known as the H Cup in France due to restrictions on alcohol sponsorship) was launched in the summer of 1995 on the initiative of the then Five Nations Committee - now the Six, in order to provide a new level of cross border competition. Twelve teams from Ireland, France, Wales, Italy and Romania took part in the 1995/96 tournament which consisted of just 15 matches. England and Scotland elected not to play in the tournament. The competing teams played in four Pools of three with the group winners going directly into the semi-finals. In the final, played in front of a crowd of 21,800 at Cardiff Arms Park on 6 January, 1996, Toulouse defeated Cardiff 21-18 to become the first champions of Europe. Teams from England and Scotland joined the competition in 1996/7 to make it a truly European event.

1997–98 saw the introduction of a home and away format in the pool games. The five pools of four teams, which guaranteed each team a minimum of six games, and the three quarter-final play-off matches all added up to a 70-match tournament. Brive reached the final again but were beaten late in the game by Bath with a penalty kick. Ironically, English clubs had decided to withdraw from the competition in a dispute over the way it was run which meant Bath were unable to defend the crown.

Without English clubs, the 1998–99 tournament revolved around France, Italy and the Celtic nations. Sixteen teams took part in four pools of four. French clubs filled the top positions in three of the groups and for the fourth consecutive year a French club, in the shape of Colomiers from the Toulouse suburbs, reached the final. Despite this it was to be Ulster's year as they beat Toulouse (twice) and reigning French champions Stade Français on their way to the final at Lansdowne Road, Dublin. Ulster then carried home the trophy after a 21–6 win over Colomiers in front of a capacity 49,000 crowd.

English clubs returned in 1999–2000. The pool stages were spread over three months to allow the competition to develop alongside the nations’ own domestic competitions, and the knockout stages were scheduled to take the tournament into the early spring.