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Mr Zapata, 40, took off from Sangatte, near Calais, at 06:17 GMT on Sunday and landed in St Margaret's Bay in Dover.
The invention, powered by a kerosene-filled backpack, made the 22-mile (35.4-km) journey in 22 minutes.
Mr Zapata, a former jet-ski champion, had failed in his first attempt to cross the Channel on 25 July after complications with refuelling.
"We made a machine three years ago... and now we've crossed the Channel, it's crazy," he told reporters, before breaking into tears.
"Whether this is a historic event or not, I'm not the one to decide that, time will tell," he added.