The proposal sparked outcry last month when it was presented to city council by Boston Properties Inc., Google’s landlord, after some councilors and residents said they were surprised by losses to the park, which sits atop of a Kendall Square parking garage and is protected by an open-space covenant.

Boston Properties and Google returned to city council Monday with a revised plan that includes bumping up the amount of new park space the developer will construct in exchange for reducing the garden, and said it would contribute $2 million to design and construct that green space.

The council voted 7 to 2 in favor of Boston Properties’s proposal, which includes constructing two glass-walled connectors that will link Four, Five, and Three Cambridge Center. The developer said construction is expected to begin later this year with an expected completion date of mid-2013.