The 29 year old Cumbria native was taking part in the London Marathon on 22 April, when he collapsed just short of the finishing line at the 22.5 mile mark.
He was attended to by race medics but later died in hospital.
Campbell was running the marathon in memory of his father who died in 2016. He was hoping to raise £2,500 for youth charity Brathay Trust.
Since, hundreds of marathon runners have pledged to run the remaining 3.7 miles to “finish” the race in Campbell’s honour.
The Brathay Trust posted a tribute to Campbell on its website, which said: “Matt was a unique inspiration, a positive person whose enthusiasm and love of life touched so many. In the time we knew Matt, we were all affected by his unique personality and talent.
“We were in awe of his flair as a chef and he was generous with his time and knowledge. We were all looking ahead to working with him on some of his culinary ideas to inspire the next generation.”