....the team would make up the difference. His taxes would be paid by the team, and he would have no liability. In other words they are really paying him 37-38 million over three years.

1. The Euro clubs can pay European tax on behalf of their players.
2. In effect, this means, as some have posted above, that his salary will be somewhere north of $30 million, but he will net $20 million after European taxes are deducted.
3. He will possibly be able to exclude the $85K, as posted, from his U.S. taxable income, but this is a virtual irrelevance.
4. His U.S. taxes will be based on his gross salary, which will be over $30 million (over the three years).
5. He will be able to deduct foreign tax credit (http://en.wikipedia.org/wiki/Foreign_tax_credit) from his U.S. tax liability. Basic non-technical description of foreign tax credit (from the link above):

If a person lives in Country A, but has income sourced in Country B, he may find that both countries want to tax that income. Country A wants to tax the income because they tax the income of their residents. Country B wants to tax the income because they tax any income generated within their borders. To eliminate double taxation, the two countries have established a tax treaty saying that the country where the income is generated has the primary claim on the tax, in this case Country B. The earner would calculate and then pay tax to Country B. Next, he would calculate the amount of tax normally payable to Country A, but then reduce that tax by using the foreign tax credit to subtract the amount of tax already paid to Country B. Country A would only receive any tax if the amount paid to Country B was lower than the Country A tax, and the tax payable would be the difference between the two amounts. If the Country B tax was higher than the Country A tax, then there would be no tax paid to Country A.

6. Since U.S. tax law will view the $30M+ number as his income, it will also view the tax paid on his behalf as being paid by him, so it can all be applied to the foreign tax credit.
7. Since European taxes are typically higher than U.S. taxes, the European taxes paid on his behalf will wipe out his U.S. tax liability.

Therefore, he really will clear $20 million, or whatever the precise contract amount is, after tax.

Why do they agree to after-tax amounts, rather than just figure out what the gross amount would be and then agree to that? Perhaps to protect the player against changes in tax rates. European countries do increase tax rates.

As to employment taxes (social security), Childress is not self-employed, he is employed by a European team. So he would not be subject to self-employment taxes. He will certainly be subject to the employment taxes (social security or whatever it is called) of Greece. As in the case in the U.S. with social security, in all likelihood the employer pays part of the tax and Childress is liable for part of it. In most countries, social security taxes are limited to income below a threshold, just as in the U.S., so this is small potatoes. Even if you are correct about him being self-employed (almost certainly wrong), and fully liable for U.S. FICA taxes (probably wrong), his current liability would only be $15K a year.

But it is likely that part of the agreement is that his income is being “grossed up” enough so that he gets $20M after employment taxes as well.

I do not know, but strongly suspect that Greece has an agreement with the U.S. that excludes the U.S. from collecting employment tax (social security/self employment) on income which has been taxed in Greece (and vice versa). Most European countries do. In any event, if he is subject to any U.S. taxes, his agents will have researched it, and probably written into the agreement that he will be paid enough to ensure that he gets $20M after all taxes.

By Ian Whittell, the article suggests there is no looming exodus from the US by US citizens.

The team then has to cover the tax so that, in the case of Childress and his three-year, $20 million deal, Olympiacos reportedly is declaring a salary of about $32.5 million, with the Greek government pocketing the difference in income tax.

Of course, the other factor that the American abroad has to bear in mind is that on returning to the U.S., he must declare foreign income to the IRS and can be taxed twice - once overseas, once at home - depending on the tax arrangement between the two countries.

Additionally the ability of European clubs paying such salaries is held in doubt:

“I don’t think there would be more than three or four European teams who could make offers like that [made to Childress],” says Toronto Raptors assistant GM Maurizio Gherardini, who is Italian.

“I think Euroleague still has a lot of work to do,” says Euroleague CEO Jordi Bertomeu when asked to envision a day when Nowitzki and Gasol are playing in his league.

“The NBA offers players multimillion-dollar contracts, like Gilbert Arenas’ $111 million contract. I think it’s hard to imagine a Euroleague club reaching those kinds of numbers. But I wouldn’t rule it out … maybe one day!”

The French League recently revealed budgets for each team in the league that ranged from Le Mans at 5.63 million euros ($8.77m) to Rouen at 2.28 million euros ($3.55m).

And those figures are budgets that cover not only player salaries but also operating costs and front-office wages—hardly extravagant amounts.

There is much more in the article and well worth clicking the link and reading it all.