In the ballot of University and College Union (UCU) Scotland members, 77 percent of those who voted backed the strikes on a turnout of 66 per cent.
The university is proposing to cut 130 jobs and has refused to rule out compulsory redundancies.
Union bosses say the proposed job cuts are rushed and alternative savings haven’t been properly explored.
The planned job losses also come on the back of a further 70 jobs having already been cut in 2017.
The union said losing so many staff in such a short timescale was bound to impact on both the student experience and the university’s reputation.
The union said it remains open to negotiation, and wants to work with the employer to avoid the need for compulsory redundancies. The local branch is due to meet later this week to consider its next steps.
UCU Scotland official, Mary Senior, said: “By voting in these numbers UCU members at Heriot-Watt university have made it crystal clear today that they have no confidence in the university’s plans to cut jobs. The ballot result is a clear mandate for industrial action and to oppose job cuts.
“The employer has made good progress on seeking volunteers and should now take compulsory redundancies off the table, to give staff some job security and stability, and students the reassurances they need in the learning environment. It’s not too late for the university to avoid strike action but they need to act now.”