Do you really need a Gannt chart?
You have a collection of work (a backlog) that includes items from several projects. You need to predict the end dates of projects based on the rate at which you're actually completing work (your velocity) and on the current mix of work items, and make decisions about shuffling the backlog to move the estimate completion dates of various projects. Right so far?
Given a velocity (units of work per fixed time period), you can plan ahead by dividing your backlog items into time boxes (iterations) that hold no more than a velocity's worth of items. The time box that the last work item for a project lands in is when that project is predicted to be done. Shuffle the mix accordingly.
This is called "reality based" scheduling in some quarters, since it's based on a demonstrated rate of progress and consistent estimation. Gannt is plan based; there's a tendency to want to make reality conform to the plan, which causes a lot of stress and pain.
There are a number of Agile/Scrum tools that will automate the management of your work backlog, and let you track work and calculate velocity. I'm a fan of Pivotal Tracker, which is web-based and free. (Full disclosure: I worked with Pivotal Labs.)