They will move at the same velocity as whichever object was fastest initially.
Explanation:
If the two objects stick together after the collision and move with a common velocity, then the collision is said to be perfectly inelastic.
The momentum of course will be conserved, both the object will stick together and move together with a speed which will be more than the initial speed of the heavier body but lower than the initial speed of the lighter body in the same direction as they were moving before.
