Typically, the party who made the offer or drafted the contract signs first. This demonstrates their agreement to the terms and conditions outlined in the contract. The other party, upon receiving the signed contract, reviews it and if they agree, they sign it as well. This final signature indicates mutual consent, making the contract legally binding.
However, the signing order can change based on business practices or negotiations. A notable difference is the person signing last may have more control because they can see the signed agreement and decide if they want to agree to it. They have the final say in accepting the terms or requesting changes before signing. In saying that, both signatures are always needed to make the contract binding.