Luke Battensby lives with his girlfriend at a property on Westgate End, which has been the centre of police activity since Sunday evening.
The concerned 26-year-old watched from his window as army bomb disposal experts began searching the property, around 25m away from his home.
He said: "I knew then it could have been connected to explosion. My mind was thinking that it could be terror related, especially with everything that has gone on recently."
Mr Battensby, who works for a legal firm in the city centre, said he first noticed something was happening when he spotted an unmarked fire vehicle parked on the street outside and a police van pulled over close to HMP Wakefield.
Twenty minutes later, at around 9pm, another fire truck and police car arrived on the street, rousing his suspicion that something serious was happening.
He said: "When I first saw the unmarked fire car and police van, I didn't have any reason to suspect anything, but then more and more police started to rush to the scene.
"I saw several police officers marching quickly down the street and cordons being set up."
Mr Battensby, who has lived in Westgate End for just a month, said he was told by police that they had found "something they weren't happy with" and would be sending down the Ministry of Defence to investigate.
He said he and girlfriend Jess were told there was no immediate danger but that they should be prepared to leave if necessary.
They continued to watch as people were evacuated from other nearby premises and saw crowds start to gather at either end of the cordon.
Mr Battensby said they were asked to remain in their house, above Wakefield Floorcare, but to be visible at the windows so police could "see us and shout us if we need to move".
"It became quite busy," he said. "We were inside the cordon but we weren't asked to evacuate because we were deemed to be sufficiently far away from the property."
Counter terrorist officers are still investigating.
In a statement issued this morning, The North East Counter Terrorist Unit (CTU) said: "We can confirm that potentially suspicious material has been found at the property and examinations are ongoing.
"As a result of the discovery of the material, nearby properties were evacuated and roads were closed as a precaution in the interests of public safety."
Road closures have now been lifted in the area but a safety cordon remains in place as the CTU, supported by West Yorkshire Police, continue enquiries.
The discovery is being treated as an "isolated incident" and last night, police said it was not being treated as terror-related.
The address was searched after a 41-year-old man was arrested on suspicion of drugs offences in Leeds on Sunday.
Officers then searched the man’s home address in Westgate End. He remains in police custody