* Offer them 250K to let them know you really want them to stay while also ensuring they feel properly valued by the company, which also exceeds the external offer by high enough that the other company probably won't counter counter. If you can't offer 250K, but, say, 200K is in your budget, then also throw in some more vacation days. Also throw in a mandatory minimum severance guarantee for good measure, so they don't have to worry about layoffs.
* Offer them 250K to let them know you really want them to stay while also ensuring they feel properly valued by the company, which also exceeds the external offer by high enough that the other company probably won't counter counter. If you can't offer 250K, but, say, 200K is in your budget, then also throw in some more vacation days. Also throw in a mandatory minimum severance guarantee for good measure, so they don't have to worry about layoffs.