The Traverse City, Mich., native was 70.
"It was quiet, exquisitely tender poetry," said his daughter, Anna George Meek, of Minneapolis.
In December 2005, he was invited by the nation's poet laureate to recite and discuss his poetry at the National Library of Congress in Washington, D.C.
Among his many honors are a Guggenheim Fellowship, the Pushcart Prize and a Bush Foundation Artist Fellowship.
Meek is the author of eight books of poetry, and other works.
He holds a bachelor's degree in English from Ann Arbor's University of Michigan, 1959, and a master's degree in creative writing from New York's Syracuse University, 1963.
Meek served as a visiting professor at many colleges, such as Cambridge's Massachusetts Institute of Technology, Sarah Lawrence College in Bronxville, N.Y, and Macalester College in St. Paul. He taught at the University of North Dakota from 1984 until his retirement in 2004.
William Stobb, a former student from North Dakota who now teaches creative writing at Viterbo University in LaCrosse, Wis., said Meek "was always to the point and gentle."
"He was always focused on you working with him," Stobb said. "And he was just calmly intelligent in the way that he taught."
Michael Dennis Browne, poet and English professor at the University of Minnesota, said Meek was probably an under-acknowledged poet.
"He was a solid and gifted artist, and a real presence in the northern Plains," said Browne.
Both his daughter and his wife, Martha, of Minneapolis are poets.
"His poetry was deeply lyrical, deeply spiritual," said his wife of 41 years. "His basic value was consciousness, and his poetry is an exploration of consciousness."
In addition to his wife and daughter, he is survived by one granddaughter.
A celebration of his life will be held at 2 p.m. Sunday at the Loft Literary Center, 1011 S. Washington, Av., Minneapolis.