Meanwhile, Honduras World Cup defender Emilio Izaguirre, 24, is holding talks with the Glasgow club.
But Ledley levelled immediately, turning smartly on a cross from Emilio Izaguirre to drill home.
Thompson also had words of praise for quicksilver full-back Emilio Izaguirre, who galloped forward at every opportunity.
Hearts had a claim for a penalty turned down when Celtic defender Emilio Izaguirre clashed with David Templeton.
BBC: Hearts boss Jim Jefferies reports referee Willie Collum
Neil Lennon's side have pace and rhythm and style and, in Beram Kayal and Emilio Izaguirre, have uncovered extraordinary signings.
Ledley's winner followed a free-kick by Ki Sung-Yueng, but Butcher felt Stuart Duff had been harshly penalised for a challenge on Emilio Izaguirre.
But Neil Lennon's side levelled when Emilio Izaguirre's deflected cross was nodded on by Georgios Samaras and Ledley arrived to glance the ball past Alexander.
Emilio Izaguirre slotted home his first Celtic goal before the break, then Saints' Danny Grainger was sent off in the 87th minute for a second booking.
Despite going down to 10 men Celtic continued to put Hamilton under pressure, but Emilio Izaguirre blazed a shot wide of Cerny's right-hand post after breaking out from left-back.
Lennon thought his side started sluggishly, but he was generally delighted and picked out forward Shaun Maloney, winger Paddy McCourt, left-back Emilio Izaguirre and goalkeeper Fraser Forster for special mention.
And in the sixth minute Cha Du-Ri, playing in a more advanced role on the right of midfield, failed to connect with a superb Emilio Izaguirre cross from the left.
Brown had returned to the Celtic midfield in place of Ki Sung-Yeung, while Charlie Mulgrew, Shaun Maloney and Cha Du-Ri came in for Mark Wilson, Georgios Samaras and the injured Emilio Izaguirre.
Hearts had claims for a penalty rejected when David Templeton was challenged on the edge of the box by Emilio Izaguirre and Suso immediately forced Forster to push clear following the winger's powerful 16-yard drive.
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