You just need to use create a release definition API, and add approver in "preDeployApprovals" argument. Check the example below
"preDeployApprovals": {
"approvals": [
{
"rank": 1,
"isAutomated": true,
"isNotificationOn": false,
"approver": {
"id": "4adb1680-0eac-6149-b5ee-fc8b4f6ca227",
"displayName": "Chuck Reinhart",
"uniqueName": "Domain\\username",
"url": "http://TFS2018:8080/tfs/DefaultCollection/_apis/Identities/4adb1680-0eac-6149-b5ee-fc8b4f6ca227",
"imageUrl": "http://TFS2018:8080/tfs/DefaultCollection/_api/_common/identityImage?id=4adb1680-0eac-6149-b5ee-fc8b4f6ca227"
},
"id": 0
}
]
},