main.tf

resource "aws_api_gateway_rest_api" "api" {
  name           = "rest"
  api_key_source = "HEADER"
}

resource "aws_api_gateway_deployment" "deployment" {
  rest_api_id = aws_api_gateway_rest_api.api.id

  lifecycle {
    create_before_destroy = true
  }

  depends_on = [
    aws_api_gateway_method.method,
    aws_api_gateway_integration.integration
  ]
}

resource "aws_api_gateway_stage" "stage" {
  stage_name    = "dev"
  rest_api_id   = aws_api_gateway_rest_api.api.id
  deployment_id = aws_api_gateway_deployment.deployment.id
  # needed to prevent Terraform from updating this resource every time
  cache_cluster_size    = "0.5"
  cache_cluster_enabled = false
}

resource "aws_api_gateway_resource" "resource" {
  rest_api_id = aws_api_gateway_rest_api.api.id
  parent_id   = aws_api_gateway_rest_api.api.root_resource_id
  path_part   = "{proxy+}"
}

resource "aws_api_gateway_method" "method" {
  rest_api_id   = aws_api_gateway_rest_api.api.id
  resource_id   = aws_api_gateway_resource.resource.id
  authorization = "NONE"
  http_method   = "ANY"
}

resource "aws_api_gateway_integration" "integration" {
  rest_api_id = aws_api_gateway_rest_api.api.id
  resource_id = aws_api_gateway_resource.resource.id
  http_method = aws_api_gateway_method.method.http_method
  /* credentials             = "DO NOT SET" */
  integration_http_method = "POST"
  type                    = "AWS_PROXY"
  uri                     = aws_lambda_function.lambda.invoke_arn
}

resource "aws_lambda_function" "lambda" {
  filename      = "lambda.zip"
  function_name = "mylambda"
  role          = aws_iam_role.role.arn
  handler       = "lambda.handler"

  source_code_hash = filebase64sha256("lambda.zip")

  runtime = "nodejs12.x"

  environment {
    variables = {
      foo = "bar"
    }
  }
}

resource "aws_lambda_permission" "permission" {
  statement_id  = "AllowExecutionFromAPIGateway"
  action        = "lambda:InvokeFunction"
  function_name = aws_lambda_function.lambda.function_name
  principal     = "apigateway.amazonaws.com"

  # More: http://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-control-access-using-iam-policies-to-invoke-api.html
  source_arn = "${aws_api_gateway_rest_api.api.execution_arn}/*/*/*" // must contain full path as defined by API
}

resource "aws_iam_role" "role" {
  name = "test"

  assume_role_policy = <<EOF
{
  "Version": "2012-10-17",
  "Statement": [
    {
      "Action": "sts:AssumeRole",
      "Principal": {
        "Service": "lambda.amazonaws.com"
      },
      "Effect": "Allow",
      "Sid": ""
    }
  ]
}
EOF
}