The House voted 239-171 to pass the bill. The deal matches the $1.1bn figure adopted by the Senate last month to combat the virus.
Republican House Speaker Paul Ryan said: "This is a significant step forward in the fight against Zika. It is a responsible plan that assures the administration will continue to have the needed resources to protect the public.
"Given the urgency of the Zika threat, I hope Senate Democrats will rise above politics so we can get this done."
In February, President Obama requested $1.9bn in emergency funding to battle Zika. Democrats have however did not agree to the proposal.
The new agreement calls for $750m in spending cuts to offset the funding for Zika efforts.
The cuts include about $543m in unused funds from the implementation of President Barack Obama’s health care law and $107m in cuts to leftover Ebola funding.
The World Health Organization declared the Zika virus to be an international public health emergency.
The virus is spread to people through mosquito bites. It is generally mild and self-limiting, lasting two to seven days.
Earlier this year, researchers identified the structure of the Zika virus, a critical advance in the development of treatments.
A team from Purdue University and the National Institutes of Health used cryo-electron microscropy to create the picture of a mature Zika virus particle.
Image: Aedes aegypti – a mosquito vector of Zika virus. Photo: courtesy of Rafaelgilo.