Tavernier joined from Newcastle United following a successful loan spell with Rotherham United last season, while Spanish striker Riera was signed from Osasuna, and Rosler claims that both players perfectly fit the plans made by himself and chairman Dave Whelan.
"James is a young player with experience and in that respect he fits into the type we want to bring here in that he is young, vibrant, full of energy and determined to progress with us," the German told the club's official website.
"In Oriol, we have a proven goalscorer who has signed for us within our pay structure in the Championship and for the right fee.
"It was a complicated deal which took a lot of negotiation and the chairman also played a pivotal role."
Reports have suggested that Wigan could watch James McClean leave the club in the near future, with Derby County being tipped as a possible destination for the winger.