"Dear Michael. You are always in my prayers," wrote Hamilton. "Prayers of hope that you pull through this difficult time. You have already achieved so much, given so much."
"May God watch over you and show you the way back to your family, fans and friends."
Button’s letter recalled his strongest recollections of the racing driver.
"When I think of Michael Schumacher I think of two things," he wrote.
"The first is of one my earliest memories of being in Formula One driving out of the pitlane in Melbourne and seeing Michael’s red Ferrari ahead of me scattering the leaves as he drove beneath the trees at the approach to turn three. Even in 2000 he was already a legend.
Career in Pictures: Michael Schumacher
Career in Pictures: Michael Schumacher
1/17 February 2006
Michael Schumacher is seen in the pits during a training session at the Ricardo Tormo racetrack in Cheste near Valencia in 2006
2/17 November 1994
Hugging two team mechanics in delight for becoming World Champion Driver after the Australian Grand Prix at the Adelaide circuit in November 1994
3/17 October 1995
Flavio Briatore carries a jubilant Michael after he wins the Pacific F1 Grand Prix at Aida in Japan, and wins his second World Drivers Championshp
4/17 February 1996
Schmacher pushes his Ferrari back to the pits after engine trouble left him stranded at the entrance of the pitlane during pre-season testing at Estoril, Portugal
5/17 March 1996
During the Australian Grand Prix in Melbourne
6/17 March 1997
Michael Schumacher in the pit lane during the Australian Grand Prix at Albert Park in Melbourne, Australia
7/17 October 2000
Celebrating on the podium after winning the formula one world championship at the Japanese Grand Prix at Suzuka, Japan
8/17 July 2006
Michael Schumacher of Germany and Ferrari leads the pack into the first corner at the start of the French Formula One Grand Prix at the Nevers Magny-Cours Circuit
Lars Baron/Bongarts/Getty Images
9/17 October 2010
Michael Schumacher drives during the Korean Formula One Grand Prix at the Korea International Circuit
Clive Mason/Getty Images
10/17 October 2011
Michael Schumacher and Mercedes GP waves to the crowd as he attends the drivers parade before the Indian Formula One Grand Prix at the Buddh International Circuit on October 30, 2011 in Noida, India
11/17 December 2011
Sebastian Vettel and Michael Schumacher celebrate after winning the Nations Cup at day one of the race of champions event at the Esprit Arena
12/17 June 2012
Michael Schumacher drives at the Valencia Street Circuit on June 22, 2012 in Valencia during the first practice race of the European Formula One Grand Prix
13/17 September 2012
Michael Schumacher crashes into the back of Jean-Eric Vergne of France and Scuderia Toro Rosso during the Singapore Formula One Grand Prix in September 2012
14/17 November 2012
Schumacher drives in his last race during the Brazilian Formula One Grand Prix at the Autodromo Jose Carlos Pace
Mark Thompson/Getty Images
15/17 December 2013
Deputy director Jean Marc Grenier talks to media outside the CHU Nord hospital in Grenoble, French Alps
16/17 December 2013
Members of the staff are seen outside the emergency services at the CHU Nord hospital in Grenoble, French Alps; this is the hospital where retired seven-times Formula One world champion Michael Schumacher is reported to be hospitalized after a ski accident
17/17 December 2013
A Scuderia Ferrari and Michael Schumacher fan waits, on December 29, in Grenoble, in front of the emergency department of the Centre Hospitalier Universitaire hospital
"The second thing I think about it is that familiar red car snaking about in my mirrors. Michael was such a formidable racer relentlessly competitive - Always There.
"He’s fighting his greatest battle right now and I know everyone at Formula One will hope that he will win again. I certainly hope he will."
Car racing legend Niki Lauda also wrote Schumacher a heartfelt letter.
"Michael, every day I follow the news on your progress and every day I am close to you. I hope I will be able to talk to you very, very soon."
Schumacher's wife, Corinna, recently thanked fans for all their support in a letter published in the Grand Prix programme:
"The German Grand Prix gives me the perfect opportunity to cordially thank you for all your good wishes and positive energies you keep sending Michael," she wrote. "I have to say your sympathy blew us all away! Good to know that together we made it through the hardest time!”
Schumacher suffered near-fatal head injuries during a skiing accident in French resort Meribel in December last year. He is currently being treated at Grenoble hospital in Switzerland, near his family house.
New speculation today suggests that he could return home by the end of the month, although he will need constant support.Reuse content