Indian High Commission in Dhaka on Wednesday announced this decision in Twitter.
The Indian move came hours after Foreign Secretary Md Shahidul Haque told journalists that they had spoken to New Delhi on ways to bring back the nationals.
Yemen is on the brink of a civil war after the Houthi rebels, representing a Shia minority that makes up around a third of Yemen's population, emerged as the most powerful force in the Arabian Peninsula's poorest country last year.
They captured the capital Sana’a and ousted the country’s president.
Foreign nationals have deserted the capital. However, Bangladesh’s remained stranded as there was no Bangladesh mission in Yemen.
The government has formally approached UN migration agency IOM and talked with India that was taking back its nationals using ships.
The foreign secretary on Wednesday morning said India had agreed in principle to help Bangladesh repatriate its nationals, but after evacuating their own nationals.
After that, the High Commission tweeted: “India to Assist in Evacuation of Bangladesh Nationals from Yemen.”
According to government estimates, only between 1,500 and 3,000 Bangladeshis who mostly work with international organisations live in economically poor Yemen, which is not a preferred destination of Bangladeshi workers.
Yemenis migrate as labour force to their neighbouring countries.
Bangladesh has strongly condemned the Houthi militia action in Yemen and supports Saudi Arabia-led efforts to restore the legitimate state authority.