You can do this using Input.setSelectionRange
, part of the Range API for interacting with text selections and the text cursor:
var searchInput = $('#Search');
// Multiply by 2 to ensure the cursor always ends up at the end;
// Opera sometimes sees a carriage return as 2 characters.
var strLength = searchInput.val().length * 2;
searchInput.focus();
searchInput[0].setSelectionRange(strLength, strLength);
Demo: Fiddle