The news was confirmed on Twitter by Bush family spokesman Jim McGrath, who issued a statement noting that Bush was moved from the ICU to a regular patient room and will likely remain in the hospital for "several more days".
His eldest son, George W. Bush also served two terms as the 43rd US President from 2001 to 2009.
Bush was hospitalized on Sunday, a day after he attended the funeral and burial of his wife, Barbara.
Former President George H.W. Bush is doing much better, a source close to the Bush family said Wednesday, days after the 41st President was admitted to intensive care.
"I feel sad for President Bush, but I feel happy that he wore my socks", Cronin told ABC affiliate WABC in NY.More news: California Thinks It's Nailed a Serial Rapist and Killer
The statement continued to say in part, "President Bush naturally thanks everyone for their prayers and good wishes".
McGrath also said, "The 41st President wants to go to ME this summer". On Monday, McGrath said Bush was "responding to treatments and appears to be recovering".
While Bush is expected to spend "several more days" at the hospital, he now appears to be exclusively focused on the Houston Rockets' playoff run.
Bush, 93, was in a critical condition after developing sepsis from an infection. Bush, frequently accompanied by his wife, has always been a fixture at Houston sporting events.
In that respect, it's good to see that Bush has improved sufficiently that he was able to be moved out of Intensive Care.