Members of Aslef voted by more than four to one in favour of industrial action in an 82% turnout.
Strikes have been called for November and 21 and 27. Aslef said it expected support for the walkouts to be solid.
Adrian Thompson, human resources director at Northern Rail, said: “We are disappointed that Aslef Northern members have voted in favour of strike action despite receiving a very good pay offer of 2.7% in 2014 and 2.5% or RPI if it is higher in 2015.
“We are in continuing discussions with Aslef and have already planned to meet next week in the hope of resolving the situation.”