I guess there is some more logic in the custom web part than the editing content. Anyway, it is possible. In this case you need to use the CMSEditableRegion control in the web part. Something like this (ASCX):
<% @ Control Language="C#" AutoEventWireup="true" Inherits="CMSWebParts_General_CustomWebPart" CodeFile="~/CMSWebParts/General/CustomWebPart.ascx.cs" %>
<cms:CMSEditableRegion ID="TileTitle" runat="server" RegionType="TextBox" />
<cms:CMSEditableRegion ID="TileDesc" runat="server" RegionType="HtmlEditor" />
And then, in the code behind, it is the same as for other web parts, just do not forget to inherit from CMSAbstractWebPart class:
public partial class CMSWebParts_General_CustomWebPart : CMSAbstractWebPart