I had this question come up today and it was a little bit of work to track down so I thought I would share here.
In SharePoint 2013 the Search Service Application has something called a Global Search Center Url. In the absence of any other configuration, this is where folks will get redirected to run their queries. However if you are doing a fully scripted install using PowerShell it's not completely obvious how you set this value. Here is how you can change it:
$ssa = Get-SPEnterpriseSearchServiceApplication$ssa.SearchCenterUrl = <newURL>$ssa.Update()
Steve, thanks for sharing. Do remember that the URL to your Search Center should actually end with /Pages, i.e. if you host your search center in a host named sitecollection under "https://search.zomers.eu",
set the $ssa.SearchCenterUrl to "search.zomers.eu/Pages" (do not add a trailing slash). Otherwise your redirects from MySites will fail. If you're using a language pack on your SharePoint
farm and have created the Search Center Site Collection using a language different than an English one, replace Pages with the localized name (i.e. Seiten for Germen, Paginas for Dutch).