The chainrings should be cross compatible. You already have a long cage rear derailleur I assume with such a big cassette. Depending on differences in size of chainrings you may need to adjust chain length but I would try it first. Old school but I assume your new triple comes with axle? edit- just re-read and realized you said Ultegra so I assume that's the hollow crank which would have the axle. you do need to make sure your BB is compatible for the shimano crankset.

Ultimately compatible shifters/Frt Der/Crankset should about cover it assuming you have a nice long cage rear der.