The 26-year-old, who was with juniors Kelty Hearts, has signed for Edinburgh City in League Two.
Thomson pleaded guilty in June 2011 to inappropriate conduct towards two underage girls over the internet.
City noted his court conviction but said on Twitter they believed he deserved a second chance.
"The club acknowledges Craig's previous conviction in 2011 for offences he committed in 2010 and does not condone his behaviour in any way," they said in a statement.
"However, the club's board, management, playing staff and main sponsor collectively believe that Craig has completed his rehabilitation and we look forward to giving him the opportunity to return to playing in the SPFL."
Thomson was loaned to Lithuanian clubs Kaunas and Suduva after being fined and placed on the sex offenders' register for five years but never played for Hearts again.
After leaving Tynecastle officially in 2013, the former Scotland Under-21's potential move to Cyprus was swiftly cut short when prospective club Paphos discovered his conviction.
But he has since played for East of Scotland junior sides Arniston Rangers, Newtongrange Star and Kelty, who won the Super League last season.
Former Hearts manager Jim Jefferies, who is sporting director with Edinburgh City, stated the club would be making no further comment.

The 57-year-old, from Montrose, was killed north of Dunkeld, near Jubilee Bridge, in Perthshire.
Several other stretches of the A9 have been the scene of fatal and serious accidents this year.
November was marked by the death of a couple in a two-car crash near Dalwhinnie.
Care assistant Dennish Michael and nurse Manju Dennish, both 32 and from Inverness, were originally from India.
Earlier in the month, the parents of a five-year-old boy and three-year-old girl were taken to hospital after a crash near Calvine, in Perthshire.
In October, three people were killed in a collision near Pitlochry involving four cars. Firefighters described the accident as a "scene of carnage".
Denny couple James Forbes, 73, and his 66-year-old wife wife Anne died when their car was involved in a crash with another car.
The driver of the other car - John Potter, 63, from Scarborough - also died at the scene.
In a separate accident, Roy Greene, 41, a joiner from Kilsyth, died in a collision between a van and tipper truck near Auchterarder.
August saw the deaths of motorcyclist Peter Corris, 54, and wife Jacqueline Corris, 53, from Leyland, Lancashire.
The crash which also involved a car happened three miles south of Dalwhinnie.
Another motorcyclist, Fergus Cooney, 41, from Helmsdale, died in hospital after coming off his bike at Daviot.
Mother-of-two Sharon Topping, 38, from Moodiesburn in Glasgow, was killed after her motorbike hit the central reservation on the A9 near Pitlochry.
The accident happened just hours after buying her first motorcycle.
Her 40-year-old husband Stephen, who was travelling behind her on his own motorbike, collided with her bike and was injured.
In May, two men were injured after a coach with 37 people on board crashed north of the Berriedale Braes.
And in April, 13 elderly holidaymakers were hurt when their coach collided with a lorry near Dalwhinnie.
The same month also saw one of Scotland's most promising chefs was killed in a motorbike crash just hours before he was awarded a top accolade at the Scottish Hotel Awards.
Ryan Young, 38, who was nominated in three categories at the prestigious awards, died after his bike collided with a 4X4 vehicle.
A 44-year-old pedestrian also died after being struck by a lorry a mile north of Dunkeld.
Wintry weather affected travelling conditions earlier this year.
In February, lorry driver Andrew Raeside, of Kirkintilloch, died after his cab plunged 40ft (12m) from a bridge into a loch.
He was driving south on the A9 when his fuel lorry jack-knifed as he was crossing Coronation Bridge at Faskally.
Eight people were hurt in January in two multi-vehicle accidents.
Five cars were involved in a collision during blizzard conditions three miles south of Dalwhinnie, while the other earlier accident happened at the Cromarty Bridge.
Former Hearts full-back Craig Thomson has returned to Scottish senior football for the first time since he was convicted of a sex offence.
[NEXT_CONCEPT]
The death of lorry driver Gordon Cooper in a crash involving three articulated lorries on Thursday was the latest in a series on the A9 this year.