Human Time Diff, change mins to minutes

You can do:

echo str_replace('mins', 'minutes', human_time_diff( get_the_time('U'), current_time('timestamp') ) . ' ago');

Update:

The same using filter as suggested:

add_filter('human_time_diff', 'new_human_time_diff', 10, 2);
function new_human_time_diff($from, $to) {

    // remove filter to prevent the loop
    remove_filter('human_time_diff', 'new_human_time_diff');
    $timediff = str_replace('mins', 'minutes', human_time_diff($from, $to) . ' ago');

    // restore the filter
    add_filter( 'human_time_diff', 'new_human_time_diff', 10, 2);

    return $timediff;
}

echo human_time_diff(get_the_time('U'), current_time('timestamp'));