Is a Legal Agreement required to be done for purchasing equipments and taking ownership of Shop

I'm in the process of purchasing a bakery shop. The people who were earlier doing business in that shop had a condition that they'll vacate only if the new person purchases their bakery equipments at a good price. For this, another person agreed, he did an oral deal and bought the equipments from them but had not yet done any written agreement with these people or even a rent agreement with the landlord. In the meanwhile, I offered this second person a better price and asked him to sell me the equipments further to me and allow me to run the business here. He agreed for the sum I offered. After that, I did my rent agreement with the landlord (with this second person as a witness) and I've taken possession. Now, do I need to sign an agreement with this second person to ensure that he doesn't interfere in my business at later stage or take any steps so that the people who were earlier running the shop don't create any trouble going forward? Or is it okay if I simply pay the second person off and go ahead with the business?