The sentence was part of a plea agreement in which prosecutors dismissed more serious charges accusing Kelly Frank of planning to abduct the boy and his nanny for ransom.
Reading from a statement, Frank apologized in court Monday "for the grief that this has caused," but again denied he ever intended to carry out a kidnapping.
"In no way, shape or form was (the allegation) true, but nevertheless, it was devastating," he said.
Frank, 43, was arrested in March after investigators said he told an acquaintance of a plan to abduct Letterman's then 16-month-old son, Harry Joseph, and the nanny. The acquaintance told authorities that Frank said he believed he could extort $5 million from Letterman by holding the two for 48 hours.
Under an agreement reached with prosecutors in July, Frank pleaded guilty to felony theft for overcharging Letterman for painting, and a misdemeanor charge of obstruction for lying to investigators who initially questioned him about the alleged kidnapping plot.
Frank also pleaded guilty to an unrelated felony charge of possessing illegally killed wildlife. In exchange for the guilty pleas, prosecutors dropped charges of solicitation to kidnap.
Besides the 10-year sentence on the theft charge, a judge sentenced Frank to six months for obstruction and five years on the wildlife charge, all to be served concurrently.
Frank, who was accused of overcharging the entertainer $1,000 to $1,500 for the paint job, also was ordered to pay Letterman's ranch $1,500 and pay the state $8,000.
Teton County Attorney Joe Coble said Letterman intends to donate the $1,500 to a local charity. Letterman has not attended any of Frank's court appearances.
At the time of his arrest in March, Frank was on probation in another case in which he pleaded guilty to stalking and intimidating a woman who accused him of kidnapping and raping her.
Letterman bought the 2,700-acre Montana spread along the edge of the rugged Rocky Mountain Front in 1999.