The assignor must agree to assign their rights and duties under the contract to the assignee. The assignee must agree to accept, or "assume," those contractual rights and duties. The other party to the initial contract must consent to the transfer of rights and obligations to the assignee.
If you communicate clearly, then this is typically not an issue. This is because the seller has signed a legal and binding contract, which makes them obligated to fulfill the terms of the contract. You have every right to perform an assignment of contract when everything has been done legally.
For assignment to be effective, it must occur in the present: a promise to make a future assignment has no legal effect. No specific language is required to make such an assignment, but the assignor must make some clear statement of intent to assign clearly identified contractual rights to the assignee.
The transfer of a right from one party to another. For example, a party to a contract (the assignor) may, as a general rule and subject to the express terms of a contract, assign its rights under the contract to a third party (the assignee) without the consent of the party against whom those rights are held.