@Matthew Ryan,
Unfortunately I am still looking but I can still provide some updates because I have done some learning in the mean time :-)
It depends on a lot of factors, here are your options:
1. Hope there is a severability clause in the lease, meaning the current owner can terminate the lease at any time for any reason. That means they have to move if owner acts upon it and will be the easiest possibility for you.
2. Cash for Keys. You or current owner can talk to tenants and offer them free rent for some time period (until you move in) but then they need to move out. This could be on your dime or current owners dime. I would get this in writing and avoid a verbal agreement because they have no legal requirement to move out. I know people who have used this successfully, really depends on the tenants. If they have been there 10 years they might not want to move, even for cash.
3. Combination of these two to make sure tenants don't leave unhappy and leave a big mess (literally or financially) for you..
If you get a contract make sure it is contingent on one side of house vacating.
All my insight is from Florida area, so do some checks to make sure this is OK in your area.