With all the plumbing and wiring in place, most Moving companies (normal moving and storage firms) will do this for around $200-250 range.
If the moving companies in your area do not do reconnection (some will not, especially with gas, because of the liability issues) then either a specialty appliance and furniture delivery company (the ones that stores buy to deliver and set up furniture and appliances bought at their stores) or an Appliance Repair - Large company (though they would have to send two techs so likely to cost more like $250-350) would be other options.
Note that assuming the electric connection for the dryer (for electric, not gas dryer) matches the prong arrangement on yours (each amperage rating has a different prong arrangement so you can't hook up a mismatching dryer and outlet) this is an easy DIY job with a few friends with strong backs in exchange for pizza and beer or a movie night or such. You just have to be sure to turn off the shutoff faucets before disconnecting the hoses and realize you need to have a towel and bucket to trap the water in the hoses (leakage when disconnecting hose at faucet typically maybe 1/4 cup plus a few quarts from the hoses themselves when you lay them down), and have new hose washers to use when you reconnect the hoses. And pay attention to which is hot and cold hose. And note when the washer is tilted for carrying it will leak a bit more out of the washer (maybe a cup or so), so do that in basement before starting to move it up stairs.
Oops - you said stack - if these are stacking units fine - if regular floor units that you want stacked (pay attention to safe clearance ferom combustible materials and required ventilation clearance in manual) then you may be looking at a Handyman to build a rack to hold them. He may need to bring in another person if you are not able to cary half the weight of the appliances up the stairs with him - or rent an appliance dolly so all you are doing is helping guide and stabilize it on the stairs.
Note if using a dolly/handtruck - you need large piece of plywood (a bit larger than the appliance outside dimensions) to go under the appliance because they typically have no bottom plate, so try to handtruck them and you can damage the innards with the handtruck bottom plate tilting up in there.