Joseph and Gregory Mulhare, of Wirral, were detained on 19 November in Pattaya by Thai immigration police, it emerged.
The pair, aged 43 and 38, were held under warrants from the North West Regional Organised Crime Unit.
They are suspected of trafficking cocaine, ecstasy and methamphetamine in the UK, according to Thai police.
The Foreign Office said: “We are providing assistance to two British men following their arrest and detention in Thailand.”
Video footage of the arrests shows police armed with pistols and automatic weapons storm a room, where the brothers were sharing a bed.
‘I know I’m wanted’
It shows Joseph Mulhare cuffed on the bed in a pair of shorts, and telling officers: “I’ve only just come here on holiday.
“I know I’m wanted in England. I haven’t done anything in Thailand.”
Merseyside Police issued an appeal to trace to the brothers on 14 November.
A force spokesman said it was aware the brothers had been arrested and added: “We will be looking to speak to them when they are returned to the UK.”