"A great light has gone out in the world. Nelson Mandela was a hero of our time," the PM tweeted. "I've asked for the flag at No10 to be flown at half mast."
Barack Obama made a statement from the White House.
"He achieved more than can be expected of any man," the US president said. "He no longer belongs to us, he belongs to the angels.
"Madiba transformed South Africa and he moved all of us."
Prince William and Kate Middleton, who attended the Mandela: Long Walk to Freedom premiere on the night of his death, released a statement from the venue.
The couple paid tribute to the "extraordinary and inspiring man".
The Duke of Cambridge described the South African freedom fighter's passing as "extremely sad and tragic news" adding that their "thoughts and prayers are with him and his family."
As news spread of his sad passing, the Twitter hashtag #RIPNelsonMandela began to trend worldwide.
Former US president Bill Clinton tweeted a tribute, "I will never forget my friend Madiba."
Bill Gates took to Twitter to write, "Every time Melinda and I met Nelson Mandela, we left more inspired than ever. His grace and courage changed the world. This is a sad day. "
Chelsea Clinton added, "My thoughts and prayers are with Graça Machel & the Mandela family. We are all the richer for Madiba's extraordinary life."
Former Spice Girl Melanie C spoke of her sadness at the news: "I always feel strange acknowledging somebody's passing on twitter but I have to say I am honoured to have met the great Nelson Mandela #RIP."
Her bandmates Emma Bunton and Melanie B also expressed their sorrow. "RIP Nelson Mandela," Emma wrote. "What a legacy he has left behind. I had the honour of meeting him and his spirit was unlike any other."
"We truly have just lost someone sooo amazing in every way, what a soul, what a man, may he rest in peace, I will never forget our conversations and never forget him, today is a sad day for me," Mel added.
BBC presenter Kate Silverton said of the late leader, "I learned that courage was not the absence of fear, but the triumph over it' #NelsonMandela RIP."
Hollywood also paid its respects. "My thoughts and love go out to the Mandela family," said Charlize Theron. "Rest in Peace Madiba. You will be missed, but your impact on this world will live forever."
Samuel L. Jackson wrote, "Never met a better person in my life than Nelson Mandela. My sympathy to his family & his country."
"The privilege of spending a small amount of private time w/ Mr. Mandela as he held my baby daughter, is a highlight of my life," revealed Ryan Phillippe.
Whoopi Goldberg said, "I want 2give the world a hug I was told Mandeba just passed. Nelson Mandela R.I.P. Time for a well earned sleep.Condolences to his family."
Sports star Cristiano Ronaldo paid tribute, writing, "Thankful Madiba for your legacy and your example. You"ll always stay with us."
British boxer Amir Khan added, "Rip Nelson Mandela you will be missed by many. My heart and prayers go out to your entire family", while Jo Wood simply wrote, "God rest your soul."
Oscar-winner Goldie Hawn said, "A light has gone out in this world. RIP with the other Angels Dear Nelson."
Ian Somerhalder wrote in his touching tribute, "I'm in tears.The world has lost one of its greatest shepherds of peace.Thank you Mr.Mandela for the love you radiated."
Lionel Richie added, "Nelson Mandela was a father to all of us. May his life be a constant reminder, that we are all ONE WORLD. He will be missed - LR."
Fearne Cotton: "Mandela RIP"
AnnaSophia Robb: "Thank you #NelsonMandela for your fearless leading and inspiring the world. Your #legacy lives on."
Cindy Crawford wrote, "Rest in Peace #Nelsonmendela a true hero."
Paris Hilton: "Just landed & heard the sad new about Nelson Mandela. He was a true Hero & the world is a better place because of him. May he rest in peace."
Justin Timberlake said, "One of our GREATEST leaders... Thank you for BEING the true meaning of compassion. May you be at peace now. #RIPNelsonMandela"
Elizabeth Hurley: "RIP Nelson Mandela"
Peaches Geldof: "RIP Nelson Mandela. He changed the world, not a lot of people can say they did that."
Wyclef Jean added, "Death is something inevitable.When a man has done what he considers to be his duty to his people &his country,he can rest in peace. #Madiba"
Rafa Nadal: "Rest in peace Nelson Mandela, you have been a role model to the world. My most sincere condolences to family and friends."
Laura Whitmore: "Just heard the sad news of the death of a truly magnificent man. RIP Nelson Mandela."
Arnold Schwarzenegger: "President Mandela's life is the closest thing we have to proof of God."
Fabrice Muamba: "Thank you for everything Madiba. Rest in Peace."
Jamie Foxx: "Thank you for your mark you left on humanity Mr. Mandela. Prayers to his family, friends and the people of South Africa."