The phrase "selected based on" is correct and usable in written English. You can use this phrase when referring to a selection process; for example, "The candidates were selected based on their relevant experience.".
The students were selected based on test scores.
The rest of the music is selected based on the interaction between the host and audience.
They had been selected based on the criteria I had acquired at home.
The men's 2008 Olympic team was selected based on its performances on A.A.I. equipment.
If more than 150 qualify, entrants will be selected based on fastest times.
Seeds three and four are selected based on their finishes in the combined league.
The four employees were selected based on their interest in the project and case-worker recommendations.
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Retail Lead Linguist @ Apple Inc.