The veteran USA legend will leave Everton after 10 years of service this summer.
The former USA international has called time on his 10-year stint with the Toffees, having initially joined them on a season-long loan from Manchester United for the 2006-07 campaign.
The 37-year-old, who made 412 appearances for the Merseyside club, signed a three-year deal with the MLS outfit - whom he will be eligible to play for after July 8 - and Martinez has conceded that finding another keeper as consistent will prove very tricky.
“Tim is such an incredible character,” Martinez told Everton TV.
“In a pure goalkeeping sense his level three seasons ago when we reached the club record Premier League points tally was one of the best seasons we have had.
“The consistency in his character allows him to perform consistently and, as a performer, it will be difficult to find another as consistent as he is."
Howard, who earned 106 USA caps, lost his place to 25-year-old Spaniard Joel Robles earlier this year and has spent Everton's last eight games on the substitutes bench.
Robles has impressed since coming into the side, but it remains to be seen if Martinez views him as a long-term occupant of the number one shirt with the Goodison Park club.