Brooke Wolf Velocity pilot reported the landing gear horn and warning lights came on after takeoff. Pilot remained in traffic pattern and landed safely.

Narrative

Just after takeoff; landing gear horn and warning lights came on. On climbout; I accepted a vector from ZZZ tower and was instructed to contact ZZZ departure. Because the horn was still blaring; I asked tower if I could stay with local control until I could work out the issue with the landing gear. I offered to fly east of the airport to avoid interference with traffic in the pattern. After turning east; I was asked by the tower controller if I wanted to cancel my IFR clearance. I canceled IFR with the controller. After cycling the landing gear a couple of times; I thought that it was working correctly; but the horn and warning lights were not showing a safe condition. I asked tower for a low approach so that they could look at the state of the landing gear. My request was approved; and I was told I could overfly taxiway 1 to be closer to the tower. The tower controller said the landing gear appeared down; so I requested a landing on runway XX. The tower approved and rolled emergency equipment. I went around the traffic pattern and landed uneventfully.I taxied to the ramp and thanked the emergency responders and the tower controllers.