Since you'd said there were reasons for him to be a good choice of candidate, I didn't see the terrorists' choosing of him as a problem. So when you spoke of wanting the "transition" not to appear stupid, I took it to mean the larger transition of militancy to politics, not the smaller one of him putting the gun away, which has been done plenty of times before by all kinds of fighting men for all kinds of reasons (and talk of a "career shift" seems a bit odd to be honest -- terrorism isn't actually a job after all). And, of course, the US election proves you don't need someone who is "trained" in politics to win. You simply need someone who connects with the voters.
Anyway, if the terrorists don't have anyone better to stand for election within their ranks, then it's either him or they seek someone outside. Have they thought of looking outside the organisation? Would it be feasible? If they did have a political wing before the militant one as is usual, then it's strange they don't have someone with better political skills -- have they all died, or is no one willing to stand?
If they do have someone better -- ie someone who has political skills, is used to negotiating, is a good orator who can get people behind her, or is simply seen as a safe pair of hands -- then it's more problematic why he's chosen. Gonk's bullet points are all good ideas, but to make it seem plausible to me that he is chosen, you need to know why no one else has been. It isn't only his merits or history which are important, but that of everyone else who is or might have been picked if he wasn't around.
Also, your story's political system is relevant. Why will they have only one political representative at election? Is there only one candidate from all parties, or are they only contesting one seat, or is it a presidential style situation? Different political environments may require different skill-sets from potential candidates, as do different voting populations. If the only voters are sophisticated urban liberals, a brash candidate with no policies but a lot of skill in winding up an audience might have less chance. Conversely, a woman candidate is less likely to succeed in a world where there is no female suffrage. Is there a lot of money swirling around? If your candidate is independently wealthy, or can access funds, that might be a deciding factor.
Then there's the cultural make-up of your nation/world. Are there ethnic or religious or caste groups which always vote for their own? If so and he's a member of the largest, or a member of a group which isn't at odds with the largest, that might be crucial.
And, of course, does he want the role? Is he prepared to learn enough of politicking if he doesn't know it already? Is he fixated on terrorism as such -- ie he enjoys actually killing people -- or is he a reluctant murderer who is driven by a sense of justice or outrage? Does he kill guilty individuals as an assassin, or does he blow up pubs and leave secondary bombs to catch innocent people who are running from the first set? Those last couple of questions don't affect the plot as such, of course, but they will affect people's reaction to him, and not only the voters and media within your world, of course, but also the readers of your book.
Basically, to make his shift from terrorist to politician believable, you have to make the entire situation believable.
