Despite the terror suspicions, prosecutors said that "other motives are not being ruled out". Earlier, Mark Rutte, the Dutch Prime Minister, had said that the shooting may be linked to a family dispute.
Armed police captured Tanis after an eight-hour manhunt that brought the Netherlands' fourth largest city to a standstill amid a security lockdown.
They found a red Renault Clio that had he had used as a getaway car, and a firearm.
Reports said the two other suspects, aged 23 and 27, were brothers but unrelated to Tanis.
It emerged that Tanis, a repeat offender, had only been freed from jail in a rape case two weeks ago. He was also convicted in recent months for shoplifting and burglary.
Tanis was originally arrested in 2017 then released from pre-trial detention, before being taken back into custody when he breached his bail conditions, the central Netherlands district court said. He was freed again at the start of March.
In 2014, he was also convicted of "illegal possession of weapons" and attempted theft but acquitted of attempted manslaughter. While his relatives had links to fundamentalist Islamic groups, Tanis was reportedly known for unstable behaviour after divorcing his wife two years ago.