The decision is a huge snub to Britain, which is not apparently not considered to be in the front rank of European powers.
With French President Jacques Chirac at his side during a break in a Council of Europe summit, Mr Yeltsin said that the three countries faced similar problems and should work together to solve them.
France and Germany already hold summits every six months to co-ordinate European policy, and the trilateral summit - the first joining countries from across the former Cold War divide - marked a further step in Russia's reintegration into Europe.
"All three have common problems," said Mr Yeltsin, who, in recent weeks, has been urging Europeans to unite more against outside interference, a veiled criticism of the United States and the plan to expand the Nato alliance eastwards.
"We have agreed to meet together every year," he said. "We have agreed this was indispensable for the creation of a Grand Europe which includes Russia." Mr Chirac said he was very pleased with the decision and added: "I think this represents an important European force and a necessary element to further assure peace."
Mr Yeltsin, looking fit after his heart surgery last year, said that the time and place of the first trilateral summit had not yet been decided.
"I'll go where Jacques tells me to go and if Helmut invites us, I'll accept his invitation," he said. "I'd like to invite them too." Chirac promptly suggested the first meeting could be in Sverdlovsk, Mr Yeltsin's political power base in Siberia.
While most summit participants have limited themselves to urging the Council to do more to protect human rights, Mr Yeltsin has come to the summit to claim a central role for Russia in a new united Europe.
Left out of the European Union and Nato, he would like to see the Council play a larger role in European affairs alongside the Organisation for Security and Co-operation in Europe (OSCE). "A Europe without Russia is no Europe." he said last week.
Recognised as a key figure in ending the Cold War, the Kremlin chief has a warm reception from summit host Mr Chirac.Reuse content