Joe Gordon, a used car salesman from Colorado who was born in Thailand, admitted lese-majeste, or insulting the king, at an earlier hearing.
He was sentenced to five years in jail, but the judges halved the term because of his guilty plea.
The US consul general in Thailand said the sentence was "severe".
"He was given the sentence for his  right of expression," Elizabeth Pratt told reporters.
"We continue to respect the Thai monarchy but we also support the right of expression which is internationally recognised as a human right."
Activists say the lese-majeste law has become increasingly politicised, and is used as a tool of repression rather than as a way of protecting the monarchy.
Gordon, 55, reportedly translated parts of the widely available biography, The King Never Smiles by Paul Handley, several years ago and posted them on a blog while he was living in the US.
He was arrested in May when he visited Thailand for medical treatment.
He initially denied the charges, but said he changed his plea to guilty after being repeatedly refused bail.
After being sentenced, he told the Bangkok court: "I'm not Thai, I'm American. I was just born in Thailand. I hold an American passport. In Thailand there are many laws that don't allow you to express opinions, but we don't have that in America."
His lawyer said he would not appeal against the sentence, but would ask for a royal pardon.
Foreigners convicted of lese majeste are routinely pardoned and deported shortly after being sentenced.
Prosecutions under the law have increased dramatically in recent years, amid chronic political instability.
And the authorities have passed a new law, the Computer Crimes Act, that increases their powers to tackle any perceived insults to the monarchy on the internet or through mobile phones.
Last month a 61-year-old man was jailed for 20 years for sending four text messages that were deemed offensive to the Thai queen.
The man said he did not even know how to send a text message, and rights groups expressed serious concern about his conviction.
King Bhumibol Adulyadej, 84, is the world's longest-reigning monarch and is revered as semi-divine by many Thais.
Anybody convicted of insulting the king, queen, heir or regent faces long prison sentences.
Thailand has jailed a US citizen for two and a half years after he admitted posting web links to a banned biography of King Bhumibol Adulyadej.