main.tf

# START RESOURCE DEFINITION
resource "aws_api_gateway_resource" "HelloResource" {
  rest_api_id = "${var.gateway_api_id}"
  parent_id   = "${var.gateway_resource_parent_id}"
  path_part   = "hello"
}
# END RESOURCE DEFINITION

###############################

# START GET
resource "aws_api_gateway_method" "HelloGET" {
  rest_api_id   = "${var.gateway_api_id}"
  resource_id   = "${aws_api_gateway_resource.HelloResource.id}"
  http_method   = "GET"
  authorization = "NONE"
}

resource "aws_api_gateway_integration" "HelloGETIntegration" {
  rest_api_id             = "${var.gateway_api_id}"
  resource_id             = "${aws_api_gateway_resource.HelloResource.id}"
  http_method             = "${aws_api_gateway_method.HelloGET.http_method}"
  uri                     = "arn:aws:apigateway:${var.aws_region}:lambda:path/2015-03-31/functions/${var.lambda_arn}/invocations"
  integration_http_method = "POST"
  type                    = "AWS_PROXY"
}
# END GET

###############################

# START POST
resource "aws_api_gateway_method" "HelloPOST" {
  rest_api_id   = "${var.gateway_api_id}"
  resource_id   = "${aws_api_gateway_resource.HelloResource.id}"
  http_method   = "POST"
  authorization = "NONE"
}

resource "aws_api_gateway_integration" "HelloPOSTIntegration" {
  rest_api_id             = "${var.gateway_api_id}"
  resource_id             = "${aws_api_gateway_resource.HelloResource.id}"
  http_method             = "${aws_api_gateway_method.HelloPOST.http_method}"
  uri                     = "arn:aws:apigateway:${var.aws_region}:lambda:path/2015-03-31/functions/${var.lambda_arn}/invocations"
  integration_http_method = "POST"
  type                    = "AWS_PROXY"
}
# END POST

variables.tf

variable "gateway_api_id" {
  description = "The ID of the associated REST API"
}
variable  "gateway_resource_parent_id"  {
  description = "The ID of the Gateway Root Resource"
}

variable "lambda_arn" {
  description = "The lambda name to invoke"
}

variable "aws_region" {
  description = "The AWS region, e.g., eu-west-1"
}

variable "account_id" {
  description = "The AWS account ID"
}