I created a search page on top level of each site collection. However I would like to know how I can roll it out other team sites on different site collections.
SharePoint Designer can be used to copy a page from a site collection A to a site collection B. This is done using the SharePoint's Import Files and Export File functionalities, which become active when you select the page you'd like to work with on SPD, as seen in the figure below.
Do note, that for the page you have exported from your site collection A, you need to do a small modification before importing it to site collection B. After exporting the file, open the file in an editor of your preference to find the element
mso:PublishingPageLayout. Update the value of
mso:PublishingPageLayout to point to your destination site collection's (B) Master Page Gallery. After this is done, you can move on to importing the page to your destination.
Reference: Copy a page across different site collections.