Prof Pillinger was at his home in Cambridge when he suffered a brain haemorrhage and fell into a deep coma.
His family said he later died at Addenbrooke’s Hospital without regaining consciousness.
His death was “devastating and unbelievable”, they said in a statement.
The space scientist built a probe to search for Martian life, naming it Beagle 2 after Charles Darwin’s HMS Beagle.
It was the first time an individual researcher had sent their own vessel into space.
The spacecraft vanished without trace but Prof Pillinger carried on pushing space agencies to complete what he called “unfinished business on Mars”.
Fans took to Twitter to pay tribute to the scientist, with author Keith Mansfield calling him a “great advocate” for space and Mars.
Phil Ford, a writer on Dr Who, said: “Very sad to see Prof Colin Pillinger has died. A proper British boffin who will be fondly remembered for the Beagle Mars mission.”
At the age of 62 Prof Pillinger was diagnosed with multiple sclerosis, which left him finding it difficult to walk.
He said the illness would not diminish his efforts to land a British craft on Mars.
A professor in interplanetary science at the Open University, he headed the university’s Department of Physical Sciences until 2005.
He was awarded a CBE in 2003 and had an asteroid named after him a year later.
“A piece of Professor Pillinger now moves between Mars and Jupiter,” a Nasa scientist said at the time.
Prof Pillinger was married to Judith with whom he had two children, Shusanah and Nicolas.