The Thai-born man, who uses his American name Joe Gordon, is accused of posting a link on a blog to a royal biography banned in the country.
Lese majeste is a serious offence in Thailand, punishable by up to 15 years in prison, but defence lawyers hope the guilty plea will result in a much shorter sentence.
Judges are due to sentence Gordon on 9 November.
Gordon, 55, has previously denied the charges, media reports say, but after repeatedly being denied bail he changed his mind.
“I do not want to fight this case. I plead guilty to all the accusations,” he told judges.
There has been a series of such cases recently amid growing criticism about the way in which the law is being applied.
In June, Gordon asked US President Barack Obama for help, and US officials have expressed “disappointment” about the case.
“We are urging Thai authorities to ensure freedom of expression,” US embassy spokeman Walter Braunohler said.
King Bhumibol Adulyadej, 83, is the world’s longest-reigning monarch and is revered as semi-divine by many Thais. He has been in hospital since September 2009.
The royal family is an extremely sensitive subject in Thailand. Anybody convicted of insulting the king, queen, heir or regent faces long prison sentences.