on (one's) way
In the process of traveling to or leaving some place. We were a little late leaving the house, but we're on our way! I just want to get a drink of water, and then I'll be on my way.
*on one's way (to some place)
leaving one place for another; en route to a place. (*Typically: be ~; get ~.) I have to leave. I am on my way to the bank. I will be there soon. I'm on my way now.
on one's way
(to something or some place) Go to on the way (to something or some place).
on one's way
1. See on the way.
2. Also, be on one's way. Leave, get going, as in " On your way," said the officer, trying to move the crowd, or It's been a wonderful party but we must be on our way now. [Early 1900s]