Smith described Melissa as a "colossal mistake"
A judge in New Jersey also fined Smith $5,000 and ordered him to stay away from computer networks or the internet unless authorised by the court.
He was tracked down electronically by police and computer technicians and arrested in April 1999, a week after Melissa appeared.
Smith pleaded guilty to the charge, and on Wednesday described the creation of his virus as a "colossal mistake".
Later charge
He could have faced up to five years in prison, but prosecutors suggested a lesser term because he had assisted the authorities in thwarting other viruses.
He expects to be sentenced again on Friday on a state charge of computer theft.
"Virus writers seem emboldened by technology and enjoy the thrill of watching the damage they reap," prosecutor Christopher Christie said.
"But the case of Mr Smith and his Melissa virus should prove to others that it's a fool's game.
"Law enforcement can employ technology, too, and track down virus writers and hackers through the electronic fingerprints they invariably leave behind."
Servers hit
The virus known as Melissa - believed to have been named after a Florida stripper its creator knew - caused more than $80m in damage after it was launched in March 1999.
Computers became infected when users received a particular e-mail and opened a Word document attached to it.
It did comparatively little damage to individual computers, unlike later viruses. But it had graver implications for company and web servers carrying the huge volumes of e-mail being created.
When the document attachment was launched, a program was created which replicated the e-mail and sent it to the first 50 addresses in the Global Address Book of users running Microsoft's Outlook personal organiser.
Microsoft, Network Associates and other anti-virus and computer security companies issued warnings and supplied fixes to counteract Melissa.
It has been estimated that the virus infected more than a million computers.