The Republican White House hopeful had planned to present his running mate to journalists on Friday morning in New York, but cancelled the event after the Nice attack.
US media said Mr Pence had been selected after weeks of high level talks by Trump as he seeks to find a candidate that will help him win November's election.
Mike Pence's strong Evangelical roots will be attractive to Donald Trump who is struggling to gain the support from some Republicans.
He is a born-again Christian and has put his faith at the forefront of his politics.
"For me it all begins with faith; it begins with what matters most, and I try and put what I believe to be moral truth first. My philosophy of government second. And my politics third," he said in 2010.
Pence became well known in 2015 after he signed into law a bill that would allow businesses to refuse to serve LGBT customers.
His "religious freedom" bill in Indiana prompted protests from some but a swell in support from others.
He was forced to revise the law slightly but maintains he stands by it.
