The most common way to handle this in the US is with a UTMA account.
UTMA is the Uniform Transfers / Gifts to Minors Act ("UTMA" or "UGMA") which is a standard model law that most states have passed for special kinds of accounts.
Once you open an account, anyone can contribute. Usually parents and grandparents will contribute $13,000 or less per year to make it a tax free transfer, but you can transfer more.
The account itself would just be a standard brokerage account of any sort, but the title of the account would include your son's name, the applicable law depending on your state, and the name of the custodian who would control the account until your son turned 18.
When your son does turn 18, the money is his. Until then, the money is his, but you control how it's invested.
I'm a huge fan of Vanguard for UTMA/UGMAs. You may prefer to diversify a bit away from one company by selling the GE shares and buying an index mutual fund so that your child's education is not jeopardized by a rogue trader bringing down General Electric sometime in the next decade...