1 fortunately, luckily, propitiously, providentially, opportunely:
Happily, she made a full recovery and was soon back at work.
2 joyfully, joyously, delightedly, gleefully, cheerily, cheerfully, gaily, merrily, blithely; enthusiastically, heartily:
She waved happily as they drove off.
3 gladly, with pleasure, agreeably, contentedly, willingly, peaceably:
And they both lived happily ever after.