Financial details have not been released but technology site Red Herring reported in February that the value of the expected deal was estimated to be $23m (£11.8m).
The acquisition could eventually allow advertisers that buy online ads through Google's system to also buy ads appearing within videogames.
Advertising within videogames -- such as placing a virtual billboard on a racetrack -- is currently a small business. But games analysts believe it could become lucrative and Google's entrance into this field of advertising might give it a real boost.
San Francisco-based Adscape competes with advertising start-ups Double Fusion and IGA Worldwide, which have already signed deals with major publishers.
It also has a rival in Microsoft, which last year paid $200m for in-game ad company Massive Inc, lured by Massive's agreements to place ads in online games from UbiSoft Entertainment, THQ and Take-Two Interactive Software.
Google separately said on Friday it acquired Trendalyzer software, used to generate interactive graphics from data, from Stockholm-based Gapminder Foundation for an undiclosed sum.
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