BOSTON (AP) _ A refusenik family was embraced by tearful relatives Friday evening as they arrived in Boston after gaining permission to emigrate from the Soviet Union after the Moscow summit.

''I'm overwhelmed with gratitude toward all the people who helped me all the 11 years,'' said Yuri Zieman at Boston's Logan International Airport.

Zieman, his wife, Tatyana, and their 12-year-old daughter, Vera, were greeted by relatives and Jewish activists who worked to secure their exit visas.

''We'll drink champagne and I'll put them to bed, they didn't sleep for two days,'' said Zieman's older daughter, Galina Khatutsky, who emigrated in 1987 with her husband.

''I don't feel like it really happened because I was imagining it so many times,'' said Mrs. Zieman. ''It's still in a dream.''

U.S. diplomats said President Reagan had planned to visit the Zieman family at their Moscow apartment during the summit meeting to underscore U.S. concern for human rights in the Soviet Union.

The visit was canceled after U.S. officials were warned it could jeopardize the family's chances of emigrating.

After the summit, the Ziemans were told their request had been denied again, but a few weeks later they were granted permission to leave.

Zieman, 49, a computer specialist who lost his job when he applied to emigrate in 1977, worked as a plumber until he became ill several months ago.

Zieman had been told he was not permitted to leave the country for security reasons. He contended he never had access to state secrets and had no information that could threaten Soviet security.

The Ziemans left Moscow on Wednesday and stayed in Vienna until they left for Boston. Khatutsky, of Boston, said her parents will stay in an apartment in suburban Belmont.

A refusenik is a term applied to Soviet citizens - usually Jewish - who are refused permission to emigrate to another country.

Among the gathering of about 30 people at Logan airport was Sheila Galland of the Waltham, Mass.-based Action for Soviet Jewry. She called the release of the Ziemans a victory for the refusenik cause but said much work remains.

''There are still people waiting 10 years, 12 years,'' Galland said. She called the decision to free the Ziemans, ''a P.R. ploy,'' for Soviet leader Mikhail Gorbachev.