After deftly evading Gimli's axe after choosing the evening over the morning, he married Lothíriel, the daughter of Prince Imrahil (he literally picked a flower, since Lothíriel means 'flower maiden'), and became the King of Rohan which he stayed until his death in F.A. 63 (Merry was present at his death).
His son Elfwinë succeeded him.
Tis also mentioned in the Appendices to LOTR that "often the hooves of the Rohirrim steeds were heard on the fields of Rhûn and Harad" (or something in the like), which means that during the first years of the Fourth Age, he and Aragorn were mostly busy mopping up the lands which used to be loyal to Sauron.
Give up the Halfring, she-elf...