The former Doctor Who star plays detective Emmett Carver in Gracepoint, the US remake of Broadchurch starring Anna Gunn.
But some fans have criticised the actor’s American accent after seeing the Fox drama’s new trailer.
According to Scottish newspaper Daily Record, fans claim Tennant’s voice veers between Canadian and someone from Kentucky. Some have also reportedly called for him to revert to his Scottish accent in the drama.
Tennant said his accent was notably absent in Doctor Who and fans did not appear to mind at the time.
“If they’re fans of Doctor Who, I didn’t use a Scottish accent in that, either. I used an English accent in that,” he told the newspaper.
“I think doing different accents is part of the job of acting really. It’s something that I quite enjoy the challenge of.
“Obviously, it’s something that you take seriously, and you work with dialect coaches to help you, and then you practice until it’s in your bones.”
Kendrick Sampson, who appears in Gracepoint, said he was impressed with Tennant’s American accent.
Meet the cast of Broadchurch 2
Meet the cast of Broadchurch 2
1/12 Broadchurch 2 cast
The Broadchurch 2 cast read through Chris Chibnall's 'brilliant' new script ahead of shooting
2/12 David Tennant
He's been making the US version of Broadchurch (Gracepoint) but Tennant has been confirmed to return for the second series in Dorset. The former Doctor Who star plays DI Alec Hardy in the crime drama - but will his troubling heart problems get the better of him this time around?
3/12 James D'Arcy
James D'Arcy, known for Cloud Atlas and Hitchcock, is another new face for Broadchurch series 2. Executive producer Jane Featherstone has promised he will be a 'thrilling and important' addition
4/12 Olivia Colman
Fresh from her Best Actress win at the 2014 TV Baftas, Colman will be back as DS Ellie Miller for the second series of Broadchurch. Her character has been re-invented by Breaking Bad's Anna Gunn but Colman insists she is not 'really cross' at her stateside replacement. Colman has read the first few scripts of Broadchurch 2 and says they are 'brilliant'
5/12 Marianne Jean-Baptiste
Black British actress Jean-Baptiste, pictured here in James Baldwin’s The Amen Corner, is a new arrival on Broadchurch. Creator Chris Chibnall said he would have 'wept for months' if she had turned down a role that was specifically written with her in mind. Jean-Baptiste is set to make an 'indelible impact' on the show, apparently
6/12 Charlotte Rampling
Veteran film and TV actress Charlotte Rampling will play a new character in Broadchurch, with details being kept as hushed as possible, bar that her role will be 'integral'. 'There's none more exceptional than Charlotte' said creator Chris Chibnall
7/12 Jodie Whittaker
Whittaker will reprise her role as Beth Latimer, mother to murdered 11-year-old schoolboy Danny and friend of Ellie Miller. She was in attendance at the 2014 TV Baftas to receive the award for Best Drama Series for Broadchurch
8/12 Eve Myles
Torchwood and Frankie star Eve Myles is set for a central role in Broadchurch 2 but once again, details are being kept heavily under wraps
9/12 Arthur Darvill
Arthur Darvill will be back as local vicar and recovering alcoholic Reverend Paul Coates
10/12 Phoebe Waller-Bridge
Phoebe Waller-Bridge is known for her work in several acclaimed stage productions and is described as being 'on the way to superstardom' by Broadchurch's Chris Chibnall
11/12 Andrew Buchan
Andrew Buchan will return for Broadchurch series 2 as Danny's father Mark Latimer. Mark was one of the first suspects in the hunt for Danny's killer
12/12 Meera Syal
Meera Syal, who is renowned as a member of the team that created Goodness Gracious Me, will have a "pivotal" role in series 2
“He speaks in his original accent in between takes so to see him seamlessly go between accents was amazing. He just transforms,” he said.
The US remake, written by Broadchurch writer Chris Chibnall, has also drawn criticism for being “pointlessly similar” to the ITV original for the sake of pleasing US audiences.
Olivia Colman, who stars in Broadchurch as DS Ellie Miller, does not appear in Gracepoint despite winning a Bafta for her performance.
She is replaced by Breaking Bad’s Anna Gunn in the starring role alongside Tennant.
Gracepoint begins on Fox in the US on 2 October.