PC Sukh Singh, 46, joined the Met in 2009, working in the East and North East Area Basic Command Units.
Most recently he had been part of the forensic services department and was looking forward to starting a new role this month.
The father-of-two, from Ilford, caught Covid in December and lost his battle with the virus in hospital on January 26.
He leaves behind his wife Kam and teenage children Taran and Jasmeet.
Inspector Simon Ward, from the Met’s forensic services, started a fundraising page for Mr Singh’s family.
He said: “Sukh enjoyed a varied career in the MPS, serving the people of east and north east London for 12 years.
“Sukh had many friends in the MPS, creating a positive impression with all he worked with, transcending to partners within the Crown Prosecution Service who loved his ‘can do’ attitude.
“There are many positive words that have been said of Sukh. An ‘absolute diamond’, ‘a genuine guy with a cheeky grin’, ‘kind hearted and a gentle soul’ and a ‘top bloke’.”
Deputy Leader of Redbridge Council, Kam Rai, described PC Singh as a “dedicated public servant and one of the good guys”.
PC Singh is one of at least five serving Met officers who have died after contracting Covid-19.
Commissioner Cressida Dick said: “Policing is a family and the scale of our loss is truly shocking. My deepest condolences are with the families, friends and colleagues.”