Stags pair Burke and Ward have been heavily involved in Paul Carden's side over recent weeks and the Bucks boss has ensured they remain on board for the final eight games of the National League North season.
Former Republic of Ireland junior international Burke, 21, has spent a month with Telford after arriving as emergency left-back cover for the injured Brad Bood.
The former Birmingham youngster has made seven appearances so far and has been allowed to stay in Shropshire for the remainder of the campaign by his League Two parent club.
Mansfield club-mate Ward, a midfielder, already had an initial one-month deal extended after making a positive impression having arrived from Field Mill.
And Bucks chief Carden has also tied down his services for the remainder of the season.
Ward, who is also 21, has made 13 appearances during his time at the New Bucks Head.
Telford have already handed a senior contract to prolific under-18s striker Callum Knowles on a busy deadline day for the club, with further movement set to follow before the 5pm deadline.