Former President, George Bush Senior, has offered his congratulations to Donald Trump.
Mr Bush, who did not endorse Mr Trump as the Republican Party nominee, said the president-elect and his family were in his "prayers".
Mr Bush tweeted: "Barbara and I congratulate @realDonaldTrump, wish him well as he guides America forward as our next President. His family is in our prayers."
Former US president George HW Bush has said he is "deeply saddened" to learn of the death of King Abdullah, who he describes as a "dear friend and partner".
In a statement, he said: "As President, I found His Majesty always to be a wise and reliable ally, helping out nations build on a strategic relationship and enduring friendship".
Former US President George Bush Snr has been released from hospital in Houston, Texas after being admitted on Tuesday.
A statement from his office said: "He is now resting at home, grateful to the doctors and nurses for their superb care."
Former US President George Bush Snr remains hospitalised near his home in Houston after experiencing shortness of breath this week but is "doing well", his spokesman said.
Bush, 90, was taken by ambulance to Houston Methodist Hospital on Tuesday.
Spokesman Jim McGrath said yesterday that the 41st president's prognosis was positive and that he remained hospitalised as a precaution.
The former Republican president suffers from Parkinson's disease and cannot use his legs, but he celebrated his 90th birthday in June by skydiving with a US Army parachute team.
George Bush Snr is being kept under observation as a "precaution" after struggling to breathe, his spokesman Jim McGrath said.
The 90-year-old was taken by ambulance to Houston Methodist Hospital on Tuesday evening.
It is the same hospital where he spent nearly two months in January 2013 after treatment for a bronchitis-related cough and other health issues.
Bush, who can no longer use his legs, most recently appeared seated in a wheelchair at an event in November at Texas A&M University with his son, former President George W. Bush.
Former US president George Bush Snr has been hospitalised at the age of 90 after experiencing a shortness of breath, a spokesman said.
The former US president George H W Bush has completed a 6,300 ft parachute jump celebrate his 90th birthday.
President Bush's first parachute jump took place when he was shot down over the Pacific island of Chi Chi Jima in 1944.
He says his most recent jump, the eighth he has taken, is to be his last.
Former US First Lady Barbara Bush has been cleared to leave hospital in Houston, Texas after spending nearly a week being treated for a "respiratory-related issue".
A spokesman for Mrs Bush, the wife of former President George H. W. Bush, said she had responded well to medication and was cleared to go home in the afternoon.