Roberts' transplant Thursday followed 11 days spent in the hospital and eight days of chemotherapy to prepare her for the procedure.
The donor is older sister Sally-Ann Roberts, The Associated Press reports.
Before her operation, Roberts had sent a video message to "GMA" viewers from her New York hospital bed, thanking them for their support. The message aired on Thursday's show.
Declaring that "thoughts are so powerful," Roberts told her audience, "I feel the love and I thank you for it."
In June, Roberts, 51, disclosed that she has MDS, a rare blood disorder.
Her last day on "GMA" was Aug. 30 before she began an extended medical leave from the show.