"Barbara and I wish we could have joined the U.S. delegation honoring President Mandela today. He, and his countrymen, are in our prayers," Bush, 89, wrote Tuesday.
Bush uses a wheelchair to get around now and was unable to attend the memorial for Mandela in South Africa Tuesday, ABC News reported.
Erin Lindsay, the White House deputy director of online engagement, welcomed Bush to the social media website.
"Welcome to Twitter, President @GeorgeHWBush! Can we look forward to a (Sock) Photo of the Day," she wrote.