Definitely possible. Even if you do a very gentle training programme (which I think you should) with solely the aim of getting round, you'll amaze yourself with how much your body can do.
You'll need :
A training programme. The GreatRun website has loads. Don't panic if you miss a single run, but consistency really is the name of the game for getting comfortable with running. It's much more important that you go for a run at all, than that you cover a particular speed or distance, iyswim. On a beginners programme the first few runs will be things like Monday, 5 mins, jog. Wednesday, 10 mins, jog/walk. All the little runs add up.
Trainers that fit well - it is essential that there is enough room in the toes, or your toenails will go black from repeatedly pushing against the front of your shoe. This is not usually painful, but it's not pretty either. Often this means getting a half- or full-size up from your usual. Also have a look at the bottom of a pair of shoes you wear frequently now. Is the wear on the tread more down the outside or inside edge of the foot? (outside edge = supination, inside edge = pronation. This affects what kind of shoes will suit you best) Get advice in a proper running shop.
Anti-blister socks. Worth the £8 many times over.
Sports bra. Berlei Shock Absorber Level 4 run bra is popular, and it is possible to buy extremely similar items from the far east from a well known Internet auction site for a third of the price.
If there's anywhere near you where you can run on grass or sand, do it. Increase mileage very gradually.
Be mindful of your personal safety - bear in mind when/where you are running, consider whether a hi-vis vest may be a good idea, ditto wearing headphones.
The runner's high is a real thing. Ime it kicks in after about 27 minutes, and is addictive.
Enjoy.