"Barack Obama will close the book on race, gender, group against group and straight against gay," Kennedy said, as many delegates responded with cheers and some with tears.
Kennedy is receiving treatment for brain cancer, diagnosed in May.
"The work begins anew," Kennedy said in closing, "and the dream lives on."
After a video honoring him was shown, Kennedy walked onto the stage, giving a thumbs-up sign to the cheering crowd that gave him a standing ovation.
"It is so wonderful to be here," he said, chuckling. "And nothing, nothing, is going to keep me away from this special gathering tonight."
Kennedy's niece, Caroline Kennedy Schlossberg, daughter of the late President John Kennedy, introduced the video. She said her life was changed by two men -- "Uncle Teddy" and Sen. Obama of Illinois, who is to accept the Democratic presidential nomination Thursday.
"Leaders like them come along rarely. But once or twice in a lifetime, they come along just when we need them the most," she said. "This is one of those moments."
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