Zara Al Shaikh, who has acute myeloid leukaemia, made an urgent appeal for help on Twitter in February.
A second tweet was shared more than 15,500 times.
"The relief that this day has come is overwhelming," a message from her family on Facebook read.
It was posted on the Saving Zara - Match4Zara page following the Winchester teenager's transplant on Friday.
"Best news ever! Zara has had a successful transplant and is sitting up and smiling," it said.
Her family also thanked "the wonderful kind and generous donor who this couldn't have been possible without".
Zara first went through chemotherapy in 2014 and completed four courses of the treatment, but after 15 months in remission developed acute myeloid leukaemia.
The teenager said her appeal was inspired by the #MatchForLara campaign that helped another young woman from a mixed-race background find a donor.
Among those who retweeted the appeal were Sherlock actors Mark Gatiss and Louise Brealey, as well as American author Rainbow Rowell.
Charity Anthony Nolan said a shortage of registered donors means only 20% of people from ethnic minority backgrounds who need a stem cell transplant will find a perfect match.
A spokesperson for Delete Blood Cancer had said the donor was not in the UK, but would not release any further details.
A 13-year-old girl whose social media appeal for a blood stem cell transplant went viral has had a "successful" transplant after a donor was found, her family has said.