Wireless Local Number Portability -- LNP -- enables you to keep your phone number when you switch wireless carriers, including to Boost Mobile. Boost Mobile is a prepaid division of Sprint that specializes in no-contract cell phones with pay as you go or unlimited wireless plans. Boost does not guarantee the switch to a new number, but most ports go through smoothly.
Call Boost customer service at 1-866-402-7366 and tell them you would like to port your current phone number.
Wait for the porting process to finish. The process could take up to 7 days, during which time you may have phone service on two phones.
Contact your old phone company and make sure your contract with them has been terminated.