The Bundesliga club's sporting director has confirmed that he is close to bringing the duo to the Imtech Arena in the summer to help achieve a top-half finish next season
The sporting director revealed the HSV board had approved the transfers and only personal terms needed to be agreed with the duo.
The 27-year-old Adler, whose Leverkusen contract expires in the summer, will be given a five-year deal at HSV.
Meanwhile Lech Poznan striker Rudnevs, who has attracted interest from Roma and a few Ukrainian clubs, will cost around €3.5 million and will be offered a four-year deal.
"The board has approved both transfers. Now I have to settle the last bits," Arnesen told Bild.
Hamburg finished the Bundesliga season at 15th, just six points above the relegation spots.
Arnesen, who became HSV sporing director in 2011, had previously declared his intentions to overhaul the squad in order to attain a top-eight finish.