Rangers and Dundee will need to thrash out an agreement on compensation because the Scotland under-21 cap is under the age of 23.
If there is no agreement, a tribunal will be held to decide the fee Dundee should receive.
Rangers technical director Nils Koppen said: “I am delighted that we have agreed a deal for Lyall to join the club and to continue his career at Rangers come the summer.
“Lyall has a lot of potential and I look forward to seeing him continue to grow at Rangers in the coming years.”
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Aberdeen transfer target Lyall Cameron agrees pre-contract with Rangers
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