Gray, who was selected in the fifth round, is a physical safety that will see time on special teams and could be used sparingly in passing situations.
The Bears already have signed third-round pick Roosevelt Williams, who will push for the No. 3 cornerback position and Metcalf became the second draftee to agree to terms.
Since talks with Gray and Brown are progressing Chicago must now turn their attention to signing first-round pick Marc Colombo. The 29th selection in April's NFL draft is expected to compete for the starting left tackle job with Bernard Robertson, who was selected in the fifth round of the 2000 draft.
The Bears have a recent history of not signing first-round picks by the time training camp starts. Curtis Enis, Cade McNown and David Terrell all missed practice time because of contract disputes, but those players were all top ten selections. The team expects to have all their draft choices signed before camp starts.