The shows originally set for September 7 and 8 have been moved to September 6 and September 12 respectively.
The band stated that without Tube services, it would be impossible to safely transport 82,000 people to and from the venue, preventing an event licence.
Tickets for the original dates remain valid, with refunds available for those unable to attend the new dates, and returned tickets going on general sale.
Coldplay's Wembley run will see them become the first act to play 10 dates at the stadium in the same year, with the concerts powered by 100 per cent renewable energy.