"He's a really good player who has attributes that we really like," Andrews said. "He settled into the Premier League — a new club, a new environment, a new culture — very well at West Ham last year and had some eye-catching performances.
"We obviously did more due diligence on him and his character, and how he would settle into the group. He fits what we're about with his age profile and attributes, and he comes into an already competitive squad."
The 21-year-old signed a five-year contract with a club option for a further year, joining for an initial £35m plus £5m in add-ons after Brentford's pursuit stalled earlier in the summer before talks reopened this week.
Diouf had started West Ham United's Championship opener against Burnley but was left out of the matchday squad for the following two games while the move was finalised.
Andrews was clear that Diouf's arrival does not spell the end for the options already in his squad, pointing to the versatility of the players competing for the left-back berth.
"In years gone by, we've had some injury issues there. Rico has obviously had some injury concerns over a period of time. We love Rico to bits as a player, with what he brings and the fact he's been at the club for so long and knows the culture of the club inside out," he said, before addressing how the position now shapes up.
"What we have got is really good players in that position who have different kinds of attributes. Malick comes into a competitive part of the pitch and just adds to a strong area. You've seen Keane Lewis-Potter play there at times over the last two seasons.
"Keane is versatile. It's a super strength. He's so invaluable to have within the squad. I mentioned it a couple of weeks ago — before we signed Malick — that I could envisage Keano playing in different positions this season and I don't think that will change."
Rico Henry, Lewis-Potter and Jayden Meghoma have all featured at left-back for Brentford already this season, with Lewis-Potter starting the 3-0 Premier League win over Tottenham and Henry coming into the side for the 6-1 Carabao Cup victory over Birmingham City.