Shifting careers is often hard to explain. Whether you’re moving from one department to another in your own company or starting over in an entirely different field, you’re likely to face a litany of rejoinders: Why would you want to do that? Isn’t that a little risky? Are you really qualified? Others won’t raise any outward objections, but privately, you can tell they’re skeptical.

The most important step in getting others onboard with your career transition is crafting a compelling narrative. It’s a tool often overlooked by “professional reinventers,” but it can be a critical determinant of success in winning others’ support for your professional goals and vision for the future.

When Toby Johnson graduated from West Point, her first job out of college was the furthest thing possible from entry-level paper-pushing: she became an Apache helicopter pilot, the only woman in a class of thirty trainees. Her performance won raves, but when she decided to leave the Army after seven years to attend business school, she knew she faced one big disadvantage compared to her classmates, many of whom entered with corporate experience: “The only big organization I’d ever worked for was the United States Army.” Her mission was to create a narrative that made the connections between her past and present obvious to others. She stressed the management experience she’d gained in the military (at 24 years old, she was in charge of eight $30 million Apache helicopters, plus the thirty people who managed them) and the rapid learning made possible by her early leadership experience. Now a fast-rising Fortune 500 executive, her effort succeeded.

It’s also important to identify the underlying themes that connect your professional experiences, because people generally prefer narrative continuity: a story is “better” and makes more sense to them if they see it as a logical extension of the past, rather than a rupture. When public radio executive John Davidow was appointed to head online operations at his station, it may have seemed like an unusual development for a 50-something veteran of traditional media. But he embraced the change eagerly — in part because of his sense that the new online world wasn’t a break with his media past but rather, a continuation of it. “My whole career, I’ve been a bit of a nonconformist,” he says. He began his career in TV news at the start of the satellite era and “we were in many ways defining what local television news was. There still weren’t really rules of the road.”

He sensed that same liminal potential in the online world. Even though the tools may be different (social media instead of satellite trucks), the basics of creating a powerful news experience are the same. So John isn’t a newbie digital executive with only a few years of experience. Instead, he argues he’s been doing the same thing for his entire career: telling stories and being a change agent.

Finally, it’s important to explain your trajectory in terms of the value you bring to others. Career transitions can sometimes be viewed as a sign of narcissism or a midlife crisis, and you don’t help that perception if you frame it as all about you. “Wanting to be fulfilled” is nice, but it’s not a valid reason for others to hand you a job or give you their business. Instead, you need to make it clear it’s not about you; it’s about the value you bring.

Libby Wagner, a poet and tenured community college professor, felt apprehensive sharing her background when she first transitioned into her new career as a management consultant. “I didn’t want anyone to know I was a poet,” she says. “I had a lot of tapes going in my head. The economists I had worked with had really talked down to me, and people in business certainly weren’t interested in what I did.” But she eventually came to realize her history wasn’t a liability, but a unique strength in her business. “The way I see the world is very language-driven,” she says. “I’m going to be listening for nuances and connections and patterns. That’s the way I look at the world and I take that to any interaction with the client, so I’ve learned to ask really good questions.” Today, Libby has consulted for Fortune 500 clients including Boeing and Nike — and she’s christened her monthly e-newsletter, The Boardroom Poet.

The first step in getting others to understand your career transition is being able to explain it to them in a compelling fashion. If you can connect the dots between your past, present, and future; identify the underlying themes in your career trajectory; and explain the unique value you can bring to your new endeavor, you’re on your way to winning their support.