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The Friedkin Conservation Fund said Roger Gower, from Birmingham, was tracking poachers on Friday in the Maswa Game Reserve.
One of his colleagues said he had been shot as he flew near the carcass of one of three elephants killed by poachers.
Charity founder Dan Friedkin said the organisation had lost "a dear friend".
The Foreign Office has confirmed the death of a UK national in Tanzania and said it was providing assistance to the family.
Pratik Patel, of the Friedkin Conservation Fund, said Mr Gower had been approaching the last of three elephants killed by poachers when he was shot.
He paid tribute to "a great guy, a great friend, a great pilot" who he said had loved working with Tanzania's wildlife.
Mr Patel said Mr Gower's main role had been flying people between the different camps on the reserve where he worked, but he had also flown daily patrols to support ground staff in their work against poachers.
Tanzanian MP Lazaro Nyalandu, a former minister for natural resources and tou that the incident had happened in the Maswa Game Reserve, which borders the Serengeti National Park in northern Tanzania.
He said Mr Gower had managed to land his helicopter, but died before he could be rescued.
Mr Nyalandu said: "RIP Capt Roger. You loved our country and I knew you on many flights we took together in defence of our wildlife heritage.
"Those poachers who killed Capt Roger are coward[s], evil, and sad people. A fine-hearted individual gone too soon, and our hearts are broken."