Twitter Inc. has agreed to give Google Inc. access to its stream of data, in a move that could make it easier for tweets to appear in search results, according to people familiar with the matter.

The deal means the 140-character messages written by Twitter’s 284 million users could be featured faster and more prominently by the search engine. The hope is that greater placement in Google’s search results could drive more traffic to Twitter, which could one day sell advertising to these visitors when they come to the site,...