Approval was given by 11-4 votes at a meeting last night, despite objections from residents and businesses.
Costa wants to move into premises occupied by Slinders Florists on the corner of Rochester High Street and Northgate.
Slinders Florists, High Street, Rochester
The double-fronted shop is in a prime location, at the crossroads leading to the cathedral and castle.
Costa plans to open up the basement and use it as a seating area.
Petitions and letters were sent to the council against the plan. Letters were received from 61 people, a paper petition with 165 signatures and two online petitions totalling 955 signatures.
Opponents are concerned about the impact that Costa will have on neighbouring independent businesses and say the introduction of the coffee shop will damage the historic character of Rochester.
The City of Rochester Society also objected, arguing that the coffee chain’s plan would erode the special retail character of the area and affect the vitality of the city centre.
Only one letter of support was received.
During the meeting, councillors opposed to the plans were worried about the proposed opening hours (6.30am to 6.30pm Monday to Friday, 7am to 6.30pm on Saturdays and 8am to 5pm on Sundays and bank holidays).
They said there were plans for a Costa in the new railway station and the chain did not need two shops so close by.
Those who supported the decision argued that the coffee chain would not damage the vitality or viability of the High Street.
Costa already has branches in Chatham High Street, Rainham High Street and Hempstead Valley Shopping Centre.