President Reagan will meet Soviet President Mikhail Gorbachev for the fifth time on Wednesday, closing out a relationship that has evolved from open hostility to the old-shoe clubbiness of rivals drawn by shared personalities.

Reagan, who spurned superpower summitry throughout his first term, is likely to accord his Soviet guest in New York the sort of personal adieu extended to Britain's Margaret Thatcher, a remarkable finale to a roller coaster tete-a-tete that survived the icy gusts of Geneva and Reykjavik to transform national policies and nuclear arsenals in just three years.Some would argue nothing has been transformed more than the attitude of the president, the longtime cold warrior who made rebuilding the U.S. military his first priority. Others say the U.S.-Soviet breakthroughs are more naturally the consequence of Gorbachev's dynamic emergence from a confusing period of leadership changes and stagnation at the Kremlin.

"I must admit that I would not have predicted after first taking office, that some day I would be waxing nostalgic about my meetings with Soviet leaders," Reagan said Saturday in his weekly radio address. "But here we are, for the fifth time, Mr. Gorbachev and I together, in the hope of furthering peace."

Wherever the credit lies, the Reagan-Gorbachev relationship has moved from unbridled suspicion, to grudging respect, to that Gentleman's Club of Two, where, according to Reagan, "there is never a sense of personal animus when the arguments are over." And now, at a luncheon at Governors Island, N.Y., Reagan will present George Bush as his membership heir in that most elite club.

In his radio speech, Reagan made a point of pushing Bush toward center stage. "No one is better versed in the details of Soviet-American relations or has a stronger foreign policy portfolio than our vice president," Reagan said.

The president said he will tell Gorbachev that Bush "stands for firmness of strength and candor in the cause of freedom," and that the "American people do not want treaties for the sake of treaties, they want agreements that endure and prevent war."

"So, on our get-together next week . . . you can be sure I'll be telling Mr. Gorbachev that George Bush represents change, yes, but also continuity," the president said.

While the administration has gone out of its way to discourage the notion that the meeting amounts to another summit, Secretary of State George P. Shultz has said "there will be lots of substantive discussion," adding that U.S. officials would welcome "forthcoming statements" by Gorbachev on troop imbalances in Europe and the Berlin Wall.

Since their initial face-off in Geneva in November 1985, Reagan, 77, and Gorbachev, 56, have held three summits, including the memorable meeting in Reykjavik, Iceland, when the two leaders actually discussed a deal to eliminate all nuclear weapons from their arsenals, only to witness the bitter collapse of their entire agenda.

Just before the Moscow summit, Reagan told interviewers from foreign newspapers and television networks that he considered Gorbachev a friend as well as an adversary.

"We can debate and we disagree. But there is never a sense of personal animus when the arguments are over."