The enzyme DNA polymerase is responsible for attaching free nucleotides to the growing DNA strand during DNA replication.

Here's how it works:

1. Recognition: DNA polymerase recognizes the existing DNA strand (template strand) and the free nucleotides.

2. Base pairing: The enzyme ensures that the incoming nucleotides pair correctly with their complementary bases on the template strand (A with T, G with C).

3. Bond formation: DNA polymerase catalyzes the formation of a phosphodiester bond between the 3' hydroxyl group of the last nucleotide on the growing strand and the 5' phosphate group of the incoming nucleotide. This adds the new nucleotide to the chain.

This process continues along the template strand, creating a new DNA strand that is complementary to the original.