Roger Bagnall, 40, was crossing Yardley Road in Acocks Green around 7pm on 19 March when he was hit by a police car responding to reports a man had been seen nearby carrying knives.
The father-of-two, who lived locally, died at the scene, the Independent Office for Police Conduct (IOPC) said.
In a statement, his family said: “On March 19 we lost a beloved partner, dad, brother and son. We are all devastated by Roger’s death.
“Roger had the biggest heart and loved to make everyone smile with his humour and wit, we loved him very much and will miss him dearly, but we take comfort in the fact his spirit will live on through his children.
“We have been overwhelmed by all the kind messages of support we have received and feel proud that Roger touched the lives of so many.”
CCTV footage has confirmed the police car’s sirens and blue lights were on at the time of the collision, the IOPC said.
It was established Mr Bagnall was not on a crossing or wearing headphones when he was struck.
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IOPC director Derrick Campbell said: “Our thoughts are with Mr Bagnall’s family and friends, and to all those affected by his death in such tragic circumstances.
“We have met with his family to explain our role, offer support and to outline the next steps of our independent investigation.
“Those inquiries are progressing and I would like to take this opportunity to thank those who came forward with CCTV footage as a result of our media appeal. This has proved valuable to our investigation.”
He added: “We would urge people not to speculate, which can be unhelpful and cause unnecessary distress.
“Our role is to independently investigate the involvement of police in this collision to establish all the circumstances surrounding it. That will include looking at any actions taken by the officers and whether those followed policy and procedure.”
