Rezaian was one of four U.S. citizens freed by Iran Sunday as part of a prisoner swap.
Ali Rezaian spoke to ABC News from Landstuhl, Germany, where Jason is receiving medical care.
"You know he's happy to be out and on his way home," he said of his brother. "He's really fortunate to have the folks here at the hospital."
Ali Rezaian said his brother has been doing "OK" despite being "neglected" for a long time. He hasn't gotten a chance to see Jason, but expects he will Tuesday. He told ABC News that Jason's doctors hadn't expressed anything "serious" about his condition to the family.
"Our main concern right now is to make sure that he integrates back in, that he gets the right psychological treatment that he needs so that he can be successful and come back home soon," Ali Rezaian said.
Washington Post Executive Editor Martin Baron and Foreign Editor Douglas Jehl sent a memo to the Post's staff, detailing their conversation with Jason Sunday.
They described Jason as being "in good spirits" and said "his mind is sharp."
"He [Jason] found escape in the fiction he was allowed to read, and today he was avidly reading whatever he wanted," they wrote.
Rezaian told his co-workers he looked forward to seeing them soon, saying, "I hear there's going to be a big party."
He landed in Geneva before flying to Ramstein Air Base in Germany with his mother and wife.