"We will do everything we can to support the families of the four British victims and ensure they get the answers and closure they deserve," he said in a statement issued by his Downing Street office.
Johnson added that Britain would work closely with Canada, Ukraine and other international partners to ensure "a comprehensive, transparent and independent international investigation and the repatriation of those who died."
"This tragic accident only reinforces the importance of de-escalating tensions in the region," he said.
"It is vital that all leaders now pursue a diplomatic way forward."
Iranian President Hassan Rouhani said a military probe into the tragedy had found "missiles fired due to human error" brought down the Boeing 737, calling it an "unforgivable mistake".
Supreme leader Ayatollah Ali Khamenei offered his condolences and ordered the armed forces to address "shortcomings" so that such a disaster does not happen again.
The acknowledgement came after officials in Iran had categorically denied Western claims that the Ukraine International Airlines airliner had been downed in a catastrophic error.
The incident occurred hours after Iran launched a wave of missiles at bases hosting American forces in Iraq in response to the killing of Qasem Soleimani, one of Iran's top generals, in a US drone strike.
The majority of passengers on the flight PS752 were dual national Iranian-Canadians but also included Ukrainians, Afghans, Britons and Swedes.