1. Do they have a lease? The lease will most likely be enforced.
2. Do they intend on staying? Eviction could take months and hopefully they don't do damage to the property.
3. Is offering them cash for keys an option?
I'd talk to a real estate attorney and an agent you can trust.
Once you have purchased the property and have title you can approach the tenant. Offer keys for cash is the quickest way to get them out. Or start the eviction process. The main objective here is getting the tenant out without them destroying the property. And yes the tenant does have rights, you want to pursue this legally.
Every situation is a bit different. Is the seller telling you that the home is subject to the "tenant's rights"? Is the seller going to handle getting the tenants out prior to the closing?
If your offer is accepted and getting the tenants out is up to you, then I would go to the home and let them (tenant's) know that you are purchaisng the home and would like to ask them what their intentions are. Also tell them that you will be closing on the home in 30 days and would like them out as soon as possible.
If they refuse to leave, you will have to go through the legal system to get them out and it is a step by step process that you can do on your own if you like. You just have to hope that the tenants will not damage the property once they leave, especially if the eviction happens AFTER your closing. It is a delicate situation and I would advise you, yes, be nice and see what happens.
If the tenants are not receptive, maybe offer them a small incentive to move out without damaging anything, such as a moving allowance or something. But if they are difficult, then use the legal process, you will win, it will just take some time and money.
Thanks and Good Luck,