Here is an implementation that streams the file's content out without buffering it (buffering in byte[] / MemoryStream, etc. can be a server problem if it's a big file).

public class FileResult : IHttpActionResult
{
    public FileResult(string filePath)
    {
        if (filePath == null)
            throw new ArgumentNullException(nameof(filePath));

        FilePath = filePath;
    }

    public string FilePath { get; }

    public Task<HttpResponseMessage> ExecuteAsync(CancellationToken cancellationToken)
    {
        var response = new HttpResponseMessage(HttpStatusCode.OK);
        response.Content = new StreamContent(File.OpenRead(FilePath));
        var contentType = MimeMapping.GetMimeMapping(Path.GetExtension(FilePath));
        response.Content.Headers.ContentType = new MediaTypeHeaderValue(contentType);
        return Task.FromResult(response);
    }
}

It can be simply used like this:

public class MyController : ApiController
{
    public IHttpActionResult Get()
    {
        string filePath = GetSomeValidFilePath();
        return new FileResult(filePath);
    }
}