Brentz is a left-handed pitcher from Parkway South Senior High (Mo.) and Tellez is a first baseman from Elk Grove High (Calif.).
With the exception of Bickford, the Blue Jays have now signed every one of their top-16 selections. They've signed 18 of their top-20 and 26 of their top-30 as well. Overall, the team agreed to deals with 28 of its 40 selections from the Draft.
It became clear late in the week that Bickford was unlikely to sign. When asked on Thursday why that was the case, general manager Alex Anthopoulos hinted that there are factors at play aside from just money.
The recommended slot value for the 10th selection is more than $2.9 million.
Anthopoulos went out of his way to praise Bickford's character and lamented the fact that he was limited to what he could say publicly about the negotiations.
The only way a team can receive a compensatory pick is if it offers at least 40 percent of the recommended slot value, but Anthopoulos wouldn't disclose the exact amount Toronto was willing to pay.
There has been speculation that there could have been an issue with Bickford's medical records, which teams do not have access to prior to the Draft.
This is the second time in three years the Blue Jays were unable to sign their top pick. The club was also unable to reach an agreement with right-hander Tyler Beede after the 2011 Draft.
Bickford is a 17-year-old right-hander who finished his senior year with a 1.72 ERA, while allowing 44 hits and recording 159 strikeouts in 99 1/3 innings. He will attend Cal State Fullerton.
Derek Wetmore is an associate reporter for MLB.com.. This story was not subject to the approval of Major League Baseball or its clubs.