"Amman criminal court today initially condemned the 28-year-old Pakistani to death by hanging but immediately reduced the sentence to 10 years in jail after the families of the victims, also from Pakistan, dropped all legal claims against him," the official told AFP.
"He was charged with premeditated murder after he shot dead his 16-year-old wife and her alleged lover, who is also 16, in the Jordan Valley in 2013."
The man handed himself in to police and "confessed that he suspected the two had an affair and said he wanted to cleanse his honour," the official added.
Between 15 and 20 women are murdered in honour killings in Jordan each year, despite government efforts to curb such crimes.
In Pakistan, hundreds of women are murdered by their relatives each year in the defence of "honour".
Last year, 869 women died in such killings there, according to the independent Human Rights Commission of Pakistan.