You can use Force.com REST APIs to get the list of All Approval Processes, Submit a Record for Approval, approve a Record, reject a Record or for bulk Approvals. The Getting Started with Force.com REST API guide has detailed documentation with examples and you might want to check it out.
Use the Process Approvals resource to submit a record or a collection
of records for approval. Each call takes an array of requests. The
entity must support an approval process and an approval process must
have already been defined.
In the following example, the record "001D000000I8mIm" is submitted for approval process "PTO_Request_Process" by skipping its entry criteria on behalf of submitter "005D00000015rZy."
Example request body submit.json file
{
"requests" : [{
"actionType": "Submit",
"contextId": "001D000000I8mIm",
"nextApproverIds": ["005D00000015rY9"],
"comments":"this is a test",
"contextActorId": "005D00000015rZy",
"processDefinitionNameOrId" : "PTO_Request_Process",
"skipEntryCriteria": "true"}]
}
Example JSON response body
[ {
"actorIds" : [ "005D00000015rY9IAI" ],
"entityId" : "001D000000I8mImIAJ",
"errors" : null,
"instanceId" : "04gD0000000Cvm5IAC",
"instanceStatus" : "Pending",
"newWorkitemIds" : [ "04iD0000000Cw6SIAS" ],
"success" : true } ]