Final answer:
The enzyme responsible for covalently linking nucleotides together during DNA replication is DNA polymerase, which adds nucleotides to the growing DNA chain by forming covalent phosphodiester bonds.
Step-by-step explanation:
The enzyme that covalently links nucleotides together during DNA replication is DNA polymerase. This enzyme is crucial for the DNA synthesis process, as it adds deoxyribonucleotides, each complementary to a nucleotide on the template strand, to the 3'-OH group of the growing DNA chain. The other enzymes mentioned such as Helicase, DNA gyrase, and DNA topoisomerase, have different roles in DNA replication. Helicase is responsible for unwinding the DNA double helix, DNA gyrase and topoisomerases relax the DNA from supercoiled structures, and in addition to polymerization, DNA ligase is specifically involved in joining Okazaki fragments on the lagging strand.