The 35-year-old Croat, who had played at Hamburg from 2007 to 2009 and then joined Bayern Munich until 2012, had asked for the transfer himself, Wolfsburg said.
"When Ivica came to us we told me we consider him as an important player for us. But his wish was to transfer was too big so we agreed to it," sports director Klaus Allofs said.
Allofs had earlier said a deal with the 24-year-old World Cup winner Schuerrle, who joined Chelsea in 2013 but has struggled to carve out a regular starting spot, was still pending.
"Fact is this morning that all signatures are still missing and I am an old-fashioned guy so it is not done yet," Allofs told ZDF Television's morning news programme.
"That is why we are not announcing them yet. For Schuerrle there are still some things to be settled. It is now out in the open that we are making efforts but it is still not a done deal yet."
Wolfsburg, who take on leaders Bayern Munich later on Friday as the Bundesliga resumes after the winter break, are second in the league, 11 points behind the Bavarians.
Hamburg, in 14th place, are hoping Olic's scoring and experience will lift them away from the relegation zone.
(Reporting by Karolos Grohmann; Editing by Amlan Chakraborty and Pritha Sarkar)
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