Veleno scored a goal on two shots and added two hits in Wednesday's 6-4 win over the Flyers.
Veleno logged an assist and two hits in Saturday's 4-2 win over the Maple Leafs.
Veleno was held off the scoresheet for the 13th game in a row in Thursday's 4-1 loss to the Flyers.
Veleno scored a goal in Wednesday's 4-1 win over the Blackhawks.
Veleno signed a two-year, $5.5 million contract with the Red Wings on Friday, per Elliotte Friedman of Sportsnet.
Veleno finished with 12 goals, 16 assists and a minus-16 rating through 80 games of the 2023-24 campaign.
Veleno (head) will play Thursday versus the Coyotes, Ansar Khan of MLive.com reports.
Veleno posted an assist and six PIM in Saturday's 5-0 win over the Flames.
Veleno provided an assist in Saturday's 5-3 win over the Kings.
Veleno (undisclosed) will be back in the lineup versus Boston on Sunday.