Microsoft was first off the mark, launching today in a beta version, available in the US only.
Microsoft said the Twitter agreement on Bing will see tweets relating to search terms appear and automatically update on the search page.
Users can also click on 'See more tweets about' and go to a full page of results from Twitter, where they will be ranked based on factors like the number of followers the Twitterer has and whether or not the tweet has been written elsewhere.
It will not index tweets from protected accounts or if they have been deleted.
Microsoft is doing all it can to push Bing as a real competitor to Google, so being first with a Twitter agreement — even only for a few hours — is widely seen as a coup.
Nonetheless, Google quickly followed Microsoft's news with its own announcement, saying it had reached an agreement with Twitter to include updates in Google search results.
This follows other changes to Google's search to make it more 'real time' such as highlighting the search terms that are currently most popular, instead of hiding them away in a separate part of the Google website.
Marissa Mayer, vice-president of search products and user experience at Google, said in the official Google blog: "We believe that our search results and user experience will greatly benefit from the inclusion of this up-to-the-minute data, and we look forward to having a product that showcases how tweets can make search better in the coming months."
It is not clear when the Google Twitter search will go live.
Microsoft has also done a deal with , which will see search engine index status updates and make them searchable. This is not expected to go live for a few months, according to reports.