All draft picks are free to sign. There is going to be a set number of years for each round pick.
1st rounds= 5 years
2nd rounds= 4 years
3-5th rounds= 3 years
6th rounds= 2 years
7th rounds= 1 year
Make sure you have room to sign all of your draft picks, if you do not, they will get put in the FA pool. Max team roster is 55 guys, so post roster cuts before the end of the draft if you need to in order to sign your draft picks.