The Riyadh court also sentenced another defendant to eight years in jail after finding him guilty of taking part in protests and publishing anti-regime posts online, SPA said in a report late Monday.
SPA did not identify the defendants who it said have 30 days to file their appeals.
The tweeter was also banned from travel and handed a 100,000 riyal ($27,000) fine, the report said.
The defendant, accused of "adopting extremist ideology", had contacted "so-called reformers", urged anti-regime protests, and took part in a demonstration which he filmed and published on social networks, said SPA.
The second defendant was convicted of trying to assist a Shiite protester wounded during clashes with police in the flashpoint village of Awamiya in the Shiite-populated Qatif district.
He was found to have joined the funeral of an activist shot dead by security forces, during which he chanted anti-regime slogans with other protesters demanding punishment against policemen involved in the killing, according to SPA.
He also published anti-regime posts online and supported "saboteurs" in Qatif, site of sporadic unrest sparked by the kingdom's Shiite minority since 2011.
The kingdom's interior ministry on Friday published a list of "terror" groups which analysts have warned could further affect civil liberties in the absolute monarchy.
On the list is the Muslim Brotherhood, Al Nusra Front, which is Al Qaeda's official Syrian affiliate, and the Islamic State of Iraq and the Levant, another jihadist group fighting in Syria and Iraq.
It also includes the little-known Saudi Hezbollah Shiite militant group and the Shiite Huthi rebels in neighbouring Yemen.
The ministry said it will prosecute those who back such groups "financially or morally", or seek to promote them in the media and on social networks.
It also forbids "participation in, calling for, or incitement to fighting in conflict zones in other countries" as well as calling for demonstrations or taking part in them.