The bill heads to Republican Gov. Susana Martinez, who supports a statewide ban against texting by drivers.
The measure cleared its final hurdle in the Legislature on Tuesday when it passed the House 62-1. It was previously approved by the Senate.
The proposal will prohibit drivers from sending or reading text messages and emails, or making Internet searches from smartphones or other handheld wireless devices. There would be a $25 fine for a first violation and $50 for subsequent violations.
Forty-one other states ban texting by all drivers.
New Mexico already prohibits texting for teenage drivers with a learner's or provisional license.