Siggery, who stands at 6ft 3in and weighs 16 stone, is a product of the Scarlets academy and has spent the last 18 months playing in the Welsh Premiership.
The move sees Siggery become the second young Scarlet to join the Exiles following their signing of fly-half Steven Shingler.
"Moving to London Irish is a positive step for me. Quite a few of the young lads at the club made a big impact last season and I hope to do the same when I join next season," he said.
Siggery and Shingler played for Wales in Tuesday's record 92-0 defeat to New Zealand Under-20s at the Junior World Championship in Italy.
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