The state-run KUNA news agency flashed news of Bush's death Saturday morning at the age of 94.
Kuwait's ruling emir, Sheikh Sabah Al Ahmad Al Sabah, offered his condolences to Bush's son, the former President George W Bush. Sheikh Sabah also offered condolences to current President Donald Trump.
KUNA said Sheikh Sabah noted Bush's efforts to "create a new international order based on justice and equality among nations."
Sheikh Sabah also said Bush never "forgot the Kuwaiti people and will remain in their memory." Former President Bill Clinton is remembering George HW Bush for his "great long life of service, love and friendship."
In a statement issued early Saturday, Clinton said he would be "forever grateful" for the friendship he formed with the man he turned out of the White House after one term.
Clinton, who defeated Bush in the 1992 presidential election, says he was always struck by Bush's "innate and genuine decency" and by his devotion to his wife Barbara and his family.
Clinton says Bush's extensive record of public service was rare, with his years in the military, in Congress, the United Nations, China, the CIA and as vice president and president.
Clinton adds that Bush never stopped serving even after leaving office, working on tsunami relief in Asia and within the US after Hurricane Katrina.
The two former presidents worked together on those relief efforts.
Brent Scowcroft, the national security adviser during George HW Bush's presidency, said "The world has lost a great leader" and "this country has lost one of its best."
Scowcroft said in a statement that he was "heartbroken" at losing a man a man he called "one of my dearest friends."
Texas Gov. Greg Abbott said the state joins the nation in mourning "the passing of one of our greatest Presidents."
In a brief statement, the Republican said "George HW Bush was an American hero and icon. He was a friend to all he met. He embodied class and dignity." Abbott added that "Texans are genuinely honored that he called the Lone Star State home and we collectively grieve this monumental loss."
President Donald Trump and first lady Melania Trump are mourning the passing of former President George HW Bush.
In a statement, the Trumps praise Bush for his "sound judgment, common sense and unflappable leadership."
The Trumps say that Bush "inspired generations of his fellow Americans to public service."
They also praise the former president for guiding the nation and the world to a "peaceful and victorious conclusion of the Cold War."
The Trumps add that Bush remained humble despite his accomplishments, "following the quiet call to service that gave him a clear sense of direction."
The statement was issued while the Trumps are in Buenos Aires, Argentine for the Group of 20 summit.
James A. Baker III, former President George HW Bush's secretary of state and longtime confidant, said his friend's legacy "will be forever etched in the history of America and the world." He noted Bush's "lifelong record of selfless patriotic service to our nation," from being the youngest US Navy aviator in World War II to serving as a Texas congressman, United Nations ambassador, the first US ambassador to China, CIA director, vice president and president.
In a statement, Baker said that in each position, Bush "led with strength, integrity, compassion and humility - characteristics that define a truly great man and effective leader." Baker added that, "with a singularly unique consistency, he always demonstrated these traits, whether on the global stage or interacting with people in his everyday life. His passion was a deep love of family and our country."
Praise is coming in for former President George H.W. Bush from another former president.
The office of former President Barack Obama and Michelle Obama said Bush's life was "a testament to the notion that public service is a noble, joyous calling. And he did tremendous good along the journey."
The Obamas credited him with "expanding America's promise to new immigrants and people with disabilities. Reducing the scourge of nuclear weapons and building a broad international coalition to expel a dictator from Kuwait. And when democratic revolutions bloomed across Eastern Europe, it was his steady, diplomatic hand that made possible an achievement once thought anything but - ending the Cold War without firing a shot."
They said: "It's a legacy of service that may never be matched, even though he'd want all of us to try."
Former President George HW Bush has died at the age of 94.
Family spokesman Jim McGrath says Bush died shortly after 10 pm Friday, about eight months after the death of his wife, Barbara Bush.
The nation's 41st president served from 1989 to 1993, and eight years later watched his son George W. became the 43rd president.
The elder Bush saw his popularity swell with the United States' success in the Gulf War in 1991, only to watch it evaporate in a brief but deep recession. The Republican was defeated in his bid for a second term by Democrat Bill Clinton.
Bush had also been a World War II hero, Texas congressman, CIA director and Ronald Reagan's vice president.
Only one other US president, John Adams, had a son who also became president.