Another way, if you're really in love with the piece and want to keep it: Small "L" brackets. Use waferboard/plywood along the back, the going under it into the load bearing areas and all the corners and use smalls "L" brackets and screws to shore it up even further. Another bit of advice: get a can/tube of construction adhesive to lock everything together.^ This is good advice, which I will employ next time. I don't think I have ever had a piece of flat packed furniture which has survived any of my many house movings.
Wafer, brackets, nails, and glue you're talking-- if you shop around-- maybe 12 bucks in parts, $20 tops (USD off course, local currency will vary).