Kennedy, 76, had planned to address the graduates - including stepdaughter Caroline Raclin - Sunday in Middletown, Conn. The commencement exercises coincide with 25th reunion festivities for his son, Edward Kennedy Jr., who graduated from the school in 1983.
The Massachusetts Democrat decided against making the trip after suffering a seizure last Saturday and undergoing a brain biopsy on Monday. A malignant brain tumor was diagnosed on Tuesday.
As he did immediately after returning home, Kennedy went sailing Thursday. He spoke briefly to reporters at his home in Hyannis Port, saying that he felt "very well" and that the hospital workers had been "just spectacular."
"We received an incredible amount of wonderful notes and letters from friends and colleagues in the Senate, as well as people here in Massachusetts," he said.
The senator said the outpouring of support he received, which included honks and waves from drivers on his way home and hand-lettered signs in his neighborhood, have been "very uplifting, very touching. And I'm grateful for all that."
Obama, who leads in the race for the Democratic presidential nomination, said he and Kennedy had talked earlier in the week about the Illinois senator delivering the commencement speech. Kennedy has endorsed Obama in his race against fellow Democrat Hillary Rodham Clinton and has campaigned for Obama.
"Considering what he's done for me and for our country, there's nothing I wouldn't do for him," Obama said in a statement. "So I'm looking forward to standing in his place on Sunday, even though I know I won't be able to fill his shoes."
Spokeswoman Stephanie Cutter said Kennedy accepted Obama's offer to help "knowing it would be an historic opportunity for the school and all those attending. ... He's enormously grateful to Sen. Obama and the support he's received from all of his colleagues this last week."
Kennedy will not attend the graduation ceremonies, remaining at his family compound on Cape Cod. He returned to Hyannis Port on Wednesday after being released from Massachusetts General Hospital.
The senator will still keep long-standing plans to host Raclin, daughter of his wife, Vicki, at a dinner Saturday night. Also expected at the dinner are her siblings, grandparents and aunts and uncles.
Congress is on a Memorial Day recess next week, although it is unclear when Kennedy will return to Capitol Hill. His doctors are weighing chemotherapy and radiation regimens, but no further announcement is expected from them before midweek.